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REAL-TIME TASK SCHEDULING UNDER THERMAL CONSTRAINTS
A Dissertation
by
YOUNGWOO AHN
Submitted to the Office of Graduate Studies ofTexas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
August 2010
Major Subject: Computer Engineering
REAL-TIME TASK SCHEDULING UNDER THERMAL CONSTRAINTS
A Dissertation
by
YOUNGWOO AHN
Submitted to the Office of Graduate Studies ofTexas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Approved by:
Co-Chairs of Committee, Riccardo BettatiNarasimha Reddy
Committee Members, Weiping ShiDeepa Kundur
Head of Department, Costas Georghiades
August 2010
Major Subject: Computer Engineering
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ABSTRACT
Real-Time Task Scheduling under Thermal Constraints. (August 2010)
Youngwoo Ahn, B.S.; M.S., Seoul National University
Co–Chairs of Advisory Committee: Dr. Riccardo BettatiDr. Narasimha Reddy
As the speed of integrated circuits increases, so does their power consumption.
Most of this power is turned into heat, which must be dissipated effectively in order
for the circuit to avoid thermal damage. Thermal control therefore has emerged as an
important issue in design and management of circuits and systems. Dynamic speed
scaling, where the input power is temporarily reduced by appropriately slowing down
the circuit, is one of the major techniques to manage power so as to maintain safe
temperature levels.
In this study, we focus on thermally-constrained hard real-time systems, where
timing guarantees must be met without exceeding safe temperature levels within the
microprocessor. Speed scaling mechanisms provided in many of today’s processors
provide opportunities to temporarily increase the processor speed beyond levels that
would be safe over extended time periods. This dissertation addresses the problem
of safely controlling the processor speed when scheduling mixed workloads with both
hard-real-time periodic tasks and non-real-time, but latency-sensitive, aperiodic jobs.
We first introduce the Transient Overclocking Server, which safely reduces the
response time of aperiodic jobs in the presence of hard real-time periodic tasks and
thermal constraints. We then propose a design-time (off-line) execution-budget al-
location scheme for the application of the Transient Overclocking Server. We show
that there is an optimal budget allocation which depends on the temporal character-
iv
istics of the aperiodic workload. In order to provide a quantitative framework for the
allocation of budget during system design, we present a queuing model and validate
the model with results from a discrete-event simulator.
Next, we describe an on-line thermally-aware transient overclocking method to
reduce the response time of aperiodic jobs efficiently at run-time. We describe a mod-
ified Slack-Stealing algorithm to consider the thermal constraints of systems together
with the deadline constraints of periodic tasks. With the thermal model and temper-
ature data provided by embedded thermal sensors, we compute slack for aperiodic
workload at run-time that satisfies both thermal and temporal constraints. We show
that the proposed Thermally-Aware Slack-Stealing algorithm minimizes the response
times of aperiodic jobs while guaranteeing both the thermal safety of the system and
the schedulability of the real-time tasks. The two proposed speed control algorithms
are examples of so-called proactive schemes, since they rely on a prediction of the
thermal trajectory to control the temperature before safe levels are exceeded.
In practice, the effectiveness of proactive speed control for the thermal man-
agement of a system relies on the accuracy of the thermal model that underlies the
prediction of the effects of speed scaling and task execution on the temperature of
the processor. Due to variances in the manufacturing of the circuit and of the envi-
ronment it is to operate, an accurate thermal model can be gathered at deployment
time only. The absence of power data makes a straightforward derivation of a model
impossible.
We, therefore, study and describe a methodology to infer efficiently the thermal
model based on the monitoring of system temperatures and number of instructions
used for task executions.
v
To my family
vi
ACKNOWLEDGMENTS
I would like to thank my research advisor, Dr. Riccardo Bettati, for his guid-
ance and support during all these years. I am greatly indebted to him for his constant
inspiration, encouragement, and patience throughout my doctoral study. His excep-
tional commitment to research and strong demand for excellence have guided me this
far. And his valuable feedback contributed greatly to the improvement and progress
of my research and dissertation.
I thank the rest of my dissertation committee members: Dr. Narasimha Reddy,
Dr. Weiping Shi, and Dr. Deepa Kundur. I also thank Dr. Paul Gratz, who substi-
tutes for Dr. Weiping Shi at my defense. Their insightful comments and constructive
criticism helped me to improve the dissertation in many ways.
I would like to thank Dr. Lauren Cifuentes for her support with my graduate
assistantship, and Mr. Willis Marti for his kind guidance in the VTECH project.
Many thanks also go to my fellow workers for the project. They are: Mr. Omar
Alvarez, Ms. Rene Mercer, Mr. Hutson Bets, Mr. Garg Kapil, Mr. Gaurav Yadav,
and Ms. Jillian Michelle.
I would like to express my appreciation to Dr. Inchoon Yeo. His constant
eagerness for research always stimulated me to work harder and the discussion with
him improved my research as well. In addition, I thank my friends and fellow students
at Texas A&M University for numerous discussions related to my research work. I
sincerely thank all the current and previous members in Real-Time Systems Group:
Dr. Shenquan Wang, Dr. Pubali Banerjee, Mr. Omar Alvarez, Mr. Ja-Ryeong Koo,
Mr. Chien An Lai, Mr. Tuneesh Lella, Mr. Saswat Mohanty, and Mr. Animesh
Pathak. Special thanks to Dr. Shenquan Wang for his comments and guidance in
this research field.
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Last but not least, I thank my parents and my family members for their contin-
uous support and encouragement. I am especially grateful to my wife for her endless
support and love. Without their tremendous sacrifices and great love, I would not
have chance for successfully accomplishing my Ph.D.
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TABLE OF CONTENTS
CHAPTER Page
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1. Increasing Power Density of Microprocessors . . . . . 1
2. Thermal Impact on Microprocessors . . . . . . . . . . 3
3. Thermal Management of Microprocessors . . . . . . . 3
4. Thermal Issues in Real-Time Systems . . . . . . . . . 5
B. Overview of Research Problems and Contributions . . . . . 6
C. Dissertation Organization . . . . . . . . . . . . . . . . . . 9
II BACKGROUND AND RELATED WORK . . . . . . . . . . . . 10
A. System Model . . . . . . . . . . . . . . . . . . . . . . . . . 10
1. Power Model . . . . . . . . . . . . . . . . . . . . . . . 10
2. Thermal Model . . . . . . . . . . . . . . . . . . . . . . 12
B. Task Model . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1. Periodic Tasks . . . . . . . . . . . . . . . . . . . . . . 13
2. Aperiodic Tasks . . . . . . . . . . . . . . . . . . . . . 14
C. Scheduling of Mixed Task Set . . . . . . . . . . . . . . . . 14
D. Dynamic Speed Control for Thermal Management . . . . . 17
E. Thermal Parameter Calibration . . . . . . . . . . . . . . . 20
III TRANSIENT OVERCLOCKING FOR APERIODIC TASK
EXECUTION IN HARD REAL-TIME SYSTEMS . . . . . . . . 22
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 22
B. System Model . . . . . . . . . . . . . . . . . . . . . . . . . 23
1. Thermal Model . . . . . . . . . . . . . . . . . . . . . . 23
2. Periodic Hard Real-Time Tasks . . . . . . . . . . . . . 24
3. Aperiodic Tasks . . . . . . . . . . . . . . . . . . . . . 24
4. Thermal Steady State of System . . . . . . . . . . . . 26
C. Aperiodic Task Servers and Transient Overclocking . . . . 28
1. Bandwidth Preserving Server under Thermal Constraint 29
2. Design of Transient Overclocking Server . . . . . . . . 29
3. Budget Computations . . . . . . . . . . . . . . . . . . 30
a. Overclocking without Periodic Tasks . . . . . . . 31
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CHAPTER Page
b. Combining Periodic and Aperiodic Jobs . . . . . 36
D. Queueing Model . . . . . . . . . . . . . . . . . . . . . . . . 39
1. Arrivals and Computation Times of Aperiodic Task . 39
2. Modeling Transient Overclocking Server in Ther-
mally Constrained Environment . . . . . . . . . . . . 40
3. M/G/1 Queueing Model . . . . . . . . . . . . . . . . . 42
E. Performance Evaluation . . . . . . . . . . . . . . . . . . . 43
1. Simulations . . . . . . . . . . . . . . . . . . . . . . . . 43
2. Queueing Model Validation . . . . . . . . . . . . . . . 46
F. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IV ON-LINE THERMALLY-AWARE TRANSIENT OVERCLOCK-
ING FOR MIXED-WORKLOADS . . . . . . . . . . . . . . . . . 51
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 51
B. System Model, Assumptions and Notation . . . . . . . . . 52
1. Assumptions and Notations . . . . . . . . . . . . . . . 52
2. Periodic Hard Real-Time Task Execution . . . . . . . 53
3. Aperiodic Task Execution . . . . . . . . . . . . . . . . 55
C. Aperiodic Task Server with Transient Overclocking . . . . 63
1. Slack Stealing Server under Thermal Constraints . . . 63
2. Thermal Slack Computation . . . . . . . . . . . . . . 65
3. Speed Control . . . . . . . . . . . . . . . . . . . . . . 69
4. Dynamic Slack Reclamation . . . . . . . . . . . . . . . 74
D. Experimental Evaluation . . . . . . . . . . . . . . . . . . . 77
1. Simulation Model . . . . . . . . . . . . . . . . . . . . 77
E. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
V EFFICIENT CALIBRATIONOF THERMALMODELS BASED
ON APPLICATION BEHAVIOR . . . . . . . . . . . . . . . . . 82
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B. System Model . . . . . . . . . . . . . . . . . . . . . . . . . 84
1. Thermal Model . . . . . . . . . . . . . . . . . . . . . . 85
C. Thermal Prediction Based on Relative Utilization . . . . . 86
1. Temperature Predictions for Tasks with Dynamic
Utilization . . . . . . . . . . . . . . . . . . . . . . . . 91
D. Extensions of Thermal Prediction Model for Multicore . . 92
E. Results and Analysis . . . . . . . . . . . . . . . . . . . . . 94
1. Experimental Setup . . . . . . . . . . . . . . . . . . . 94
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CHAPTER Page
2. Experimental Results . . . . . . . . . . . . . . . . . . 94
F. Conclusion and Future Work . . . . . . . . . . . . . . . . . 96
VI CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . 99
A. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 101
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
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LIST OF TABLES
TABLE Page
I Notations for System and Task Model . . . . . . . . . . . . . . . . . 11
II Notations for Task Model . . . . . . . . . . . . . . . . . . . . . . . . 53
III Periodic Task Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
IV Experimental Systems Description . . . . . . . . . . . . . . . . . . . 94
V Average Error of Utilization Based Thermal Estimation . . . . . . . 96
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LIST OF FIGURES
FIGURE Page
1 Power density of Intel microprocessors [1] . . . . . . . . . . . . . . . 2
2 The critical instance of periodic tasks . . . . . . . . . . . . . . . . . . 23
3 Worst-case execution with aperiodic tasks . . . . . . . . . . . . . . . 25
4 Thermal steady state of system . . . . . . . . . . . . . . . . . . . . . 26
5 Erroneous slack computation leads to deadline miss . . . . . . . . . . 27
6 Temperature curves and available clock cycles . . . . . . . . . . . . . 32
7 Finding non-overclocking executing duration . . . . . . . . . . . . . . 33
8 Decrease of budget for aperiodic task server in period . . . . . . . . . 35
9 Temperature curves and available clock cycles: integration with
periodic task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
10 Approximation using average processor speed savg . . . . . . . . . . . 40
11 Comparison of average response times of aperiodic jobs without
periodic task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
12 Average response time of aperiodic jobs with execution of periodic
task: p = 200 msec . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
13 Comparison of average response times between simulation and
queueing model without periodic task . . . . . . . . . . . . . . . . . 47
14 Comparison of average response times between simulation and
queueing model with periodic task execution . . . . . . . . . . . . . . 50
15 EDF scheduling with constant speed: Γ = {(10, 2), (30, 8)} . . . . . . 55
16 Illustrations of slack computation: Γ = {(10, 4), (30, 14)} . . . . . . . 57
xiii
FIGURE Page
17 EDF scheduling with aperiodic tasks: Γ = {(10, 2), (20, 8)}, λ =
0.1, µ = 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
18 Basic idea of thermally-aware slack-stealing algorithm . . . . . . . . 64
19 The schedule of TASS algorithm: Γ = {(5, 2), (10, 4)} . . . . . . . . . 67
20 Example of TASS speed control with temperature constraint Tc =
80oC: Γ = {(10, 2), (20, 8)}, λ = 0.1, µ = 0.5 . . . . . . . . . . . . . . 70
21 RSS scheme vs. non-RSS scheme for same amount of c[tr,NTA] . . . . 72
22 Switch of speed assignment . . . . . . . . . . . . . . . . . . . . . . . 73
23 Example of an NTA interval and the NTA task queue . . . . . . . . . 75
24 Comparison of average response times according to various aperi-
odic task density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
25 Comparison of average response times of aperiodic task . . . . . . . . 80
26 Thermal trajectories with various cooling environments . . . . . . . . 83
27 Lumped RC thermal circuit model for a single-core processor . . . . 85
28 Energy density vs. average IPC . . . . . . . . . . . . . . . . . . . . . 87
29 Thermal parameter estimation & utilization based temperature
approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
30 A lumped RC thermal circuit model for dual core processors . . . . . 92
31 The temperature estimation in Intel Quad-Core Q9650 processor . . 95
32 The temperature estimation of two cores: 464.perlbench & 462.libquan-
tum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
1
CHAPTER I
INTRODUCTION
A. Motivation
In integrated circuits, such as microprocessors and graphic chips, the power con-
sumption is related to the speed of the circuit. In fact, the power density, that is
the amount of power per area that needs to be dissipated in microprocessors has in-
creased dramatically in recent years, since circuits at the same time increase in speed
and decrease in size into sub-micron regions [2]. Because the power consumption by
the microprocessors is converted into heat, resulting in significant increase of temper-
ature and unreliability of systems, appropriate mechanisms for power management
and power dissipation are becoming increasingly important.
1. Increasing Power Density of Microprocessors
The power density of modern microprocessors has been increasing due to both increase
of total power dissipation and decrease of chip feature size.
For years, there has been significant improvement in many aspects of chip tech-
nologies (e.g. performance, size, input voltage, and etc.). In the effort to improve the
performance of microprocessors with higher clock frequency or to reduce the chip fea-
ture size, we have hardly achieved an improvement in the power density until recently
in spite of the reduced supply voltage to circuits.
Fig. 1 displays the increasing trend of Intel’s microprocessor family [1]: The
power density (i.e. power dissipation per chip area) of the latest generation of single
core processor (Pentium 4 and Itanium) is very close to the level of a nuclear reactor.
The journal model is IEEE Transactions on Automatic Control.
2
Fig. 1. Power density of Intel microprocessors [1]
Although Chip-Multi-Processor (CMP) CPUs and some mobile processors mitigate
the increase of power density by running at lower clock frequencies, the trend towards
increasing power density is expected to continue along with the request for higher
performance and more aggressive computing technologies such as 3D chips [3]. With
this rapidly increasing power density, the problem of thermal management in systems
is becoming acute. Methods to manage heat to control its dissipation have been
gaining much attention by researchers and practitioners and a number of thermal
control mechanisms are routinely being used. For example, when the temperature
of Pentium 4 CPUs exceed the configured threshold temperature, the clock throttling
mechanism which is a popular thermal management technique first kicks in to lower
the thermal level. If the temperature keeps increasing to a critical level due to any
possible failure of cooling mechanism, the processor will automatically shut down as
a safety feature. To maintain the Pentium 4 CPU temperature low while it continues
executions, very powerful CPU fans are required, thereby increasing the cooling costs
and the price of systems. Power and temperature now have become the primary
3
constraints for modern processors.
2. Thermal Impact on Microprocessors
High temperatures have a significant impact on microprocessors in terms of perfor-
mance, power consumption, and reliability. Since the mobility of electrons in semi-
conductor degrades under high thermal levels, transistors work poorer than at low
temperature. And the metal resistivity of interconnections inside chips at high tem-
peratures increases so that it results in longer interconnection delay. These two can
be the main reasons for the performance degradation of microprocessors at high tem-
peratures. Furthermore, the leakage power of microprocessors grows with increasing
temperature, which in turn causes the power consumption to grow as well. It is also
known that a higher operational temperature reduces reliability and decreases the life
time of the microprocessors.
Thus, techniques are being investigated for thermal control both at design time,
through appropriate packaging and active heat dissipation mechanisms, and at run
time through various forms of Dynamic Thermal Management [4].
3. Thermal Management of Microprocessors
The design time packaging solutions (e.g. heat sinks, cooling fans, and etc.) can be
very expensive. For example, Tiwari et al. in [5] show how the incremental packag-
ing cost per additional Watt becomes very high for processors above 35-40W power
dissipation. It is also predicted that the cooling solutions through packaging only, by
which the packaging should prepare for the worst-case thermal condition, is increas-
ingly challenging. This follows because there can be very high-level of peak power
consumption in modern processors and the power density will increase extremely high
in emerging systems-on-chips. In addition, for many high-performance embedded sys-
4
tems the packaging requirements and operating environments render expensive and
bulky packaging solutions inapplicable.
Given the cost and difficulties associated with packaging-based approaches, ther-
mal control techniques that rely on containing input power at run-time are being
used. A number of Dynamic Power Management approaches to control the tempera-
ture at run-time have been proposed, which ranges from clock throttling to Dynamic
Voltage Scaling (DVS):
• Clock Throttling [6]: The clock is stalled “on-the-fly”, either to save power
consumption or to reduce the heat generation.
• Clock Gating [7]: The clock gating is one of the power-saving techniques used on
many integrated circuits. To save power, it disables unused functional units so
that their power consumption goes to zero, which enables thermal management
of architecture-level sub-components and the whole circuit as well.
• Dynamic Voltage Scaling (DVS) [4]: DVS is used in a variety of modern pro-
cessors. Switching between different frequency and voltage operating points,
microprocessors control the power consumption level and their temperature at
run-time in response to the current thermal condition. In the Enhanced Intel
SpeedStep mechanism in the Pentium M processor, for example, a low-power
operating point is reached in response to a thermal trigger by first reducing the
frequency and then reducing the voltage [6].
Most of the above Dynamic Power Management approaches to control the tempera-
ture can be considered as various forms of processor speed control mechanisms. In the
next section, we discuss how real-time systems are affected by thermal management
schemes especially by changing the speed of microprocessors, and we will lay out the
directions of our study.
5
4. Thermal Issues in Real-Time Systems
In real-time systems, the correctness of an operation depends both on its logical
correctness, and on the time by which it is performed. The classical conception is
that in a hard real-time system, the completion of an operation after its deadline is
considered at best useless and may at worst lead to a critical failure of the complete
system. A soft real-time system on the other hand will tolerate such lateness, and
may respond with decreased service quality.
Hard real-time systems are common in embedded systems interacting with physi-
cal hardwares. As an example of a hard real-time system, we can think of a car engine
control system, where a delayed response to a signal may lead to poor performance or
to failure of the engine. Some medical systems, like heart pacemakers, and industrial
process controller are good examples of hard real-time systems as well.
Live multimedia systems are typically considered to be soft real-time systems; if
the processing of a video frame gets delayed, this causes the degradation of audio or
video quality because the system either is forced to render the frame too late, thus
giving rise to display jitter, or is forced to drop the frame all together. While this
clearly affects the quality of the rendered media, the system can continue to operate
without experiencing a failure.
The various run-time thermal management mechanisms are mostly based on the
control of the microprocessor’s speed, which has clear implications for the system’s
ability to meet real-time requirements. Dynamic speed scaling allows for a trade-off
in hard real-time systems between the following two performance metrics: To meet
the deadline constraint, we run the processor at a higher speed; To maintain the safe
temperature levels, we run the process at a lower speed.
6
B. Overview of Research Problems and Contributions
In this study, we propose dynamic speed control methods for mixed workload with
both hard real-time periodic and soft real-time or non-real-time aperiodic tasks. The
control of microprocessor speed in thermally constrained systems requires an accurate
temperature model by which the thermal variations of the system can be predicted
as a function of the speed input.
In traditional systems, aperiodic jobs are often scheduled in the background, that
is, when the CPU has no hard real-time workload to execute. Additional mechanisms
are often used to trade-off execution of periodic and aperiodic portions in order to
reduce response times of aperiodic jobs without missing deadlines of periodic jobs;
this is called Slack Stealing [8]. In conventional real-time systems, jobs executing
in the background can be largely ignored when determining the schedulability1 of
real-time tasks, except for the occasional priority inversion due to non-preemptibility
of critical sections. When temperature comes into play, new forms of blocking are
introduced which are particularly problematic because the blocking occurs potentially
long after the background job has finished executing: The low-priority background
job may well be freely preemptible by incoming higher-priority jobs; the high-priority
job, however, can be affected at a later time as a result of the additional dissipated
power and ensuing higher temperatures caused by the low-priority job. The higher
temperature in turn may force the CPU to slow down, therefore affecting the high-
priority job.
This is particularly a problem in the design of techniques to handle aperiodic
job arrivals. For example, applying Slack Stealing [9] is difficult because slack must
1We say that a system is schedulable if the given periodic application system canindeed meet all its hard deadlines when scheduled according to the chosen schedulingalgorithm [8].
7
be managed both in the time and in the thermal domain: Even when there is slack
available in the time domain, using it for aperiodic jobs may unduly heat up the
processor and so trigger dynamic speed control, which in turn will delay the execution
of subsequent jobs. We say that in addition to the slack in the traditional sense, the
aperiodic job is using up thermal slack as well. Similarly, bandwidth preserving
algorithms, such as the Deferable Server [10] and others, must be adapted to take
into consideration the thermal effect of aperiodic jobs.
These complications are particularly unfortunate since transient increase of the
processor speed which we call transient overclocking would be an effective mechanism
to reduce response times of aperiodic jobs: While periodic jobs execute at safe exe-
cution speeds, for which all the periodic jobs satisfy their deadline constraints, the
processor speed can be transiently increased to provide significantly shorter response
times to aperiodic jobs. Due to the additional power dissipation during this period,
however, the temperature of the processor increases, and dynamic thermal manage-
ment is triggered, which reduces the processor speed to keep the temperature at safe
level. In this study we describe how transient overclocking can be applied to safely
reduce response times for aperiodic jobs in the presence of hard real-time periodic
tasks.
We propose both off-line and on-line mechanisms for overclocking aperiodic job
executions. For the off-line mechanism, we describe a method to allocate overclocking
budget to aperiodic workloads in a way that is efficient at run-time. This budget can
then be simply consumed similarly to that of a Deferrable Server without needing
to predict what the thermal effect of aperiodic-job execution is on the periodics at
run-time.
Although the off-line transient overclocking mechanism for aperiodic jobs effec-
tively reduces the response times of aperiodic workload, off-line designed budget-based
8
schemes are inherently conservative because they have to assume worst-case task exe-
cutions. Furthermore, off-line mechanisms run in open-loop mode and do not monitor
the temperature level of the processor. As a result they underestimate the currently
available thermal slack, which limits the reduction of job response times. We propose
an on-line speed control algorithm to further reduce aperiodic job response times by
taking early task termination and current processor temperature into account. We
combine on-line speed control with EDF task scheduling, and we describe how to as-
sign speed levels for periodic workload and aperiodic workload efficiently at run-time
without violating either delay or thermal constraint. Both off-line and on-line speed
control schemes are implemented in an event-based real-time simulation environment,
and the average response times of aperiodic jobs are are evaluated for the proposed
dynamic speed control algorithms.
For any dynamic thermal control to be effective, the availability of an efficient
and exact thermal model is essential. The thermal behavior of system is commonly
modeled using linear circuit models.
Generic thermal models only loosely capture the thermal behavior, due to vari-
ability in fabrication, environmental effects, or the need for special configurations of
either cooling devices or other aspects of packaging. When the thermal management
must deal with such variabilities, effective configuration and efficient calibration meth-
ods are needed to accurately parameterize the thermal models that drive the predic-
tive thermal control. Unfortunately, as thermal models describe the relation between
input power and thermal behavior, they rely on the availability of a measurement of
input power for parameterization purposes. Since such measurements are typically
not available at processor level in most systems, we need to find alternative ways for
thermal model calibration. We describe an indirect methodology for parameterization
of thermal models, which relies on the off-line analysis of the thermal behavior for a
9
reference application, for which we measure both the detailed utilization behavior of
the processor and its thermal behavior (through thermal sensors on the chip). We
determine and later exploit a linear relation between energy consumption and utiliza-
tion level to calibrate the thermal model for new target applications by comparing
relative utilization levels. This results in accurate thermal model parameters without
the need for power measurements. The proposed calibration methodology allows the
thermal model to be easily established, calibrated, and recalibrated at run-time to
account for different thermal behavior due to either variations in fabrication or to
varying environmental parameters. We validate the proposed methodology through
a series of experiments on a Linux platform.
C. Dissertation Organization
The rest of the dissertation is organized as follows. In Chapter II, we describe the
models on which the thermal management are based. The dynamic speed control
mechanism for thermal management is reviewed with the related work of this the-
sis. Chapter III describes our implementation of design time budget-based transient
overclocking for aperiodic task execution under thermally constrained hard real-time
systems. In Chapter IV we discuss and describe the design of on-line thermally-aware
transient overclocking approach. We show that the approach minimizes the response
times of aperiodic workload accounting for the actual thermal conditions and the pe-
riodic task executions. Chapter V presents an efficient methodology of thermal model
calibration emphasizing the importance of correct thermal modeling for the applica-
tion of proactive thermally-aware speed control. Finally, we conclude this work and
discuss future research directions in Chapter VI.
10
CHAPTER II
BACKGROUND AND RELATED WORK
Our research is based on the power model, the thermal model, the thermal manage-
ment scheme, and the scheduling of mixed task set1. In this chapter, we discuss those
system models and task model reviewing the prior work in the areas of aperiodic task
scheduling, of the dynamic thermal management mechanisms, and of thermal circuit
modelings of microprocessors.
A. System Model
The thermal effects on the real-time systems are defined by the thermal characteristics
of the computational resources and by the dynamic thermal management system. In
this section, we review how the thermal model is formulated and how the CPU speed
affects the temperature.
1. Power Model
In microprocessors, the power consumption is composed of two major sources [11, 12,
13]; Dynamic power consumption and Static power consumption.
• Dynamic power consumption Pd: The dynamic power consumption is depen-
dent on charging/discharging of gates of transistors in circuits. It is therefore
modeled as the function of processor speed, s, as follows;
Pd(s) = Ceff · V 2dd · s , (2.1)
1In the following we will make use of the notations described in Table I for systemand task model.
11
Table I. Notations for System and Task ModelSymbol Meaning
P Total power consumption of CPUPd Dynamic power consumption of CPUPs Static power consumption of CPUT (t) CPU temperature at time tTa Ambient room temperatureTc Critical temperature level (which is the thermal constraint)s CPU speedsH Maximum CPU speedsE Equilibrium CPU speed (at which the final reaching temperature of CPU is
Tc)Rth Thermal resistanceCth Thermal CapacitanceΓi A periodic taskΓi,j The jth instance of the periodic task Γipi Constant period of the periodic task Γi
ci Worst-case workload of Γi expressed in CPU clock-cycles required per instanceei The worst-case workload of Γi expressed in the execution time at the speed sEDi The relative deadline of Γi
where s = κv(Vdd−Vt)2
Vdd. Ceff , Vt, Vdd, and κv denote the effective switch ca-
pacitance, the threshold voltage, the supply voltage, and a hardware-specific
constant, respectively. All hardware-specific constants and the voltage levels
have nonnegative values. We simply describe the dynamic power consumption
as Pd(s) u κ · sα, where α ≤ 3, because the CPU speed is known to be in an
approximately linear relation with the supply voltage.
• Static power consumption Ps: The static power consumption is made by the
leakage current of microprocessors. If the processor temperature is constant, this
static power consumption is modeled as constant value. When the temperature
is related and changing, however, the static power consumption is affected and
can be modeled as a linear function of temperature [12];
Ps = δT + ρ , (2.2)
12
where δ and ρ are nonnegative constants, and T is the chip temperature.
We now represent the power consumption as P = Pd+Ps = κsα+ δT +ρ considering
both the dynamic and the static power consumptions.
2. Thermal Model
The relation between processor speed and chip-level thermal behavior can be approx-
imated at first-order by the following Fourier Model [14, 15]:
T ′(t) = αP − β(T (t)− Ta)
= ακsα − (β − αδ)T (t) + (αρ+ βTa) , (2.3)
where Ta is the environmental room temperature and assumed to have a constant
value. α is the heating coefficient and β is the cooling coefficient of microprocessors
and they represent the specific thermal characteristics of chips. If we define the
adjusted temperature as T (t) = T (t) − αρ+βTa
β−αδ, we can rewrite the equation in a
simpler form as follows,
T ′(t) =κsα(t)
Cth
− T (t)
Rth · Cth
, (2.4)
where Cth = 1αand Rth = α
β−αδ. T (t) denotes the adjusted temperature at time t (with
respect to the ambient temperature), and s(t) denotes the processor speed at time t.
In the rest of the paper, we will omit the word “adjusted” and denote T (t) simply
by T (t) except where it is unclear whether by temperature, we mean an adjusted
temperature or an actual temperature. The parameters Rth and Cth are the thermal
resistance and capacitance, respectively, and describe the thermal characteristics of
the chip. This includes packaging and heat dissipation mechanisms, such as fans.
The parameter κ and α describe the relation between speed and power requirement
13
and have some positive constant values. Typically α has a value of approximately 3.0
[14, 15].
A more compact description of the thermal behavior is as follows:
T (t) = (h⊗ sα)(t) , (2.5)
where h(t) is the impulse response function
h(t) =1
RCe−t/RC , t ≥ 0 . (2.6)
B. Task Model
Our research is centered on the thermally-aware speed control for mixed workload.
We discuss briefly in this section about the definitions and the specifics of periodic
and aperiodic tasks.
1. Periodic Tasks
The period is the amount of time between each iteration of a regularly repeated task.
Such repeated tasks are called periodic tasks. Every job in periodic tasks has to
be deadline-oriented, which means every job has to be accomplished within the set
deadline. The deadline is a constraint on the latest time at which the operation has
to come to the end. A job in a task that is released at t must complete D units of time
after t; D is the (relative) deadline of the task. We usually assume that D is equal
to the length of period p for all tasks in systems. This requirement is consistent with
the throughput requirement that the system can keep up with all the work demanded
of it all times.
One example of periodic tasks is the cruise control mechanism on an automobile.
The purpose of cruise control is to keep the speed of a vehicle constant automatically.
14
When the cruise control is active and a desired speed is set, the embedded control
system should monitor and adjust the vehicle speed regularly until the driver turns
off the cruise control mechanism. The frequency in which the computer checks and
adjusts the current speed is called as the control rate and it is fixed by the control
system designer. We can regard the cruise control as a periodic task and the periodic
speed monitoring/controls as jobs of the task.
For the periodic workload model, we consider the Liu and Layland periodic
task model [16] that defines a task Γ as (p, e), where p is the period of Γ and e is
the execution time requirement of Γ. If we need to consider the early deadlines of
periodic tasks specifically, we define each task as Γi as (pi, ei, Di).
2. Aperiodic Tasks
All real-time tasks need not to be periodic. Aperiodic tasks respond to randomly
arriving events. The jobs in an aperiodic task, however, need to be similar in the
sense that they have the same statistical behavior and the same timing requirement.
That is, their interarrival times and the execution times of jobs are identically dis-
tributed with some probability distributions respectively. To distinguish aperiodic
tasks from sporadic tasks, we say that a task is aperiodic if the jobs in it have either
soft deadlines or no deadlines [16]. For example, the processing of user inputs from
terminal application is considered as an aperiodic task since there is no deadline for
the task execution but the shorter response time is desirable.
C. Scheduling of Mixed Task Set
In the context of traditional and energy-constrained real-time systems, a variety of
approaches to scheduling a mixture of aperiodic tasks and periodic hard real-time
15
tasks have been proposed. The simplest and least effective of these is to execute
aperiodic tasks at a lower priority level than any of those with hard deadlines. This
effectively relegates aperiodic tasks to background processing. Although this method
satisfies the schedulability of periodic tasks, response times of aperiodic tasks are
prolonged unnecessarily.
A variety of dedicated scheduling servers have been proposed to handle aperiodic
tasks. As a general periodic task, the server is characterized by the pair (es, ps), where
es is the maximum budget and ps is period of the server. The simplest server is the
Polling Server (PS). PS is periodically activated and services the pending aperiodic
tasks until the budget is exhausted. The budget can be replenished again at every
activation of the server. If there is no pending aperiodic task in the task queue,
PS immediately suspends itself exhausting the budget out until it is reactivated in
the next period. Thus, if an aperiodic task arrives slightly after PS checks the empty
aperiodic task queue, the beginning of service for it is delayed until the next activation
of PS.
To overcome this unnecessary delay for aperiodic tasks, various bandwidth-
preserving servers have been proposed. They preserve their budgets even when there
is no pending aperiodic task in the queue instead of exhausting all remaining bud-
get. Whenever any aperiodic task arrives and there is budget remaining, the server
can activate and service the task. The Deferrable Server (DS)[10] is the simplest
of bandwidth preserving servers. DS works in the same way as PS except the fea-
ture of budget preservation. This feature improves the performance for the response
time of aperiodic tasks. This simple way of preserving budget, however, could make
the lower-priority periodic task miss its deadline. The Sporadic Server (SS)[17] was
proposed to resolve the problem. Using a rich combination of replenishment and con-
sumption rules, it guarantees that no periodic task miss its deadlines in the presence
16
of aperiodic tasks.
While the DS and SS are commonly used for Rate-Monotonic (RM) scheduling,
the Total Bandwidth Server (TBS)[18] and the Constant Bandwidth Server (CBS)[19]
are more suitable for Earliest-Deadline-First (EDF) scheduling. Assigning deadlines
for the aperiodic server dynamically and using their special budget replenishment
rules, they prevent aperiodic tasks from affecting the schedulability of hard real-time
periodic tasks.
In general, all bandwidth preserving servers mentioned improves responsiveness
over the polling approach. A number of problems are shared by these schemes, how-
ever: First, they tend to degrade to providing the same performance as the polling
server at high loads. Next, they are unable to make use of slack time which may be
present due to the favorable phasing of periodic tasks. Finally, they are also unable to
reclaim spare budget gained when hard real-time tasks require less than their worst
case execution time.
Lehoczky and Ramos-Thuel presented a different approach to service aperiodic
requests, known as the Slack Stealer[9] which partly addresses some of the issues with
bandwidth-preserving servers. The Slack Stealer addresses the problem of minimizing
the response times of aperiodic tasks guaranteeing that the deadlines of hard periodic
tasks are met. It steals all available slacks from periodic tasks and gives it to ape-
riodic tasks. Conceptually, it is known as the optimal aperiodic task server for the
minimization of response times. Practically, however, the complexity in realization
of the approach in a system limits its application. Thus, various approximate slack
stealing algorithms were proposed [20].
The traditional schemes of handling aperiodic tasks in real-time systems have
only the timing constraints for periodic tasks running with the aperiodic tasks. When
thermal constraints are considered, however, the increase of temperature by aperiodic
17
job execution affects the execution of periodic tasks. Since the increased temperature
means the higher possibility of slowing down of periodic job execution to keep system
temperature within the safe thermal level resulting in the delayed response time of
periodic task. Without the appropriate thermal slack computation for aperiodic task,
we should have the deadline violations of periodic tasks. In this study, we propose
the design of thermally-aware speed control algorithms for aperiodic job executions
and compare the performances.
D. Dynamic Speed Control for Thermal Management
For the safe operation of the system, the temperature must be prevented from reaching
the critical junction temperature and so destroying the processor. In our study,
we regard the system is thermally safe when the microprocessor’s temperature is
guaranteed to be equal or less than the critical temperature Tc at all times during
the task executions. The thermal safety of systems is achieved through various forms
of Dynamic Thermal Management, many of which are equivalent largely to forms of
controlling the CPU speed. For example, constant speed scaling uses a sufficiently
slow constant speed to keep the processor at a safe temperature. It has been shown
[21] that better system utilization can be achieved with dynamic speed scaling schemes.
Rao et al. [22] use variational calculus to find the optimal continuous-speed function
to optimize utilization over a given interval. They also show that a simple, two-speed
scheme approximates the optimal speed function well.
We first used a particular type of two-speed scheme, called Reactive Speed Scaling
(RSS) in [21, 23] to improve the schedulable utilization and reduce worst-case delays
in hard real-time systems: Whenever the CPU is busy, it is allowed to run at high
speed sH until it reaches a maximum temperature Tc at a safe margin from the
18
junction temperature. Once Tc is reached, the CPU continues execution at a reduced
equilibrium speed sE, which keeps the temperature at or below Tc. We next extend
to the continuous-speed scheme to apply to the online optimal speed control for the
minimization of aperiodic response time. In the continuous-speed scheme, we predicts
the job completion times and the instant at which the processor temperature reaches
Tc with the thermal model for the runtime optimization. In this study we make use
of RSS to formulate a scheme for transient overclocking of the processor to reduce the
response time of aperiodic jobs.
There is an extensive literature on dynamic speed control on processors both in
general-purpose and embedded applications. However, the majority of this literature
focuses on power management for the purpose of saving energy, not for maintaining
safe temperature levels [24, 25, 26, 27, 28, 29, 30]. While energy and temperature
are closely related, power control mechanisms for energy and temperature are quite
different. It has been shown that many energy-saving techniques do not work well
in reducing peak temperature [14, 15, 31]. This is due to the fact that energy-aware
techniques focus on dealing with the average power consumption while temperature-
aware ones focus on handling peak power consumption [15].
The work on dynamic speed scaling techniques to control temperature in real-
time systems was initiated in [14] and further investigated in [15]. Both [14] and [15]
focused on online algorithms in real-time systems, where the scheduler learns about
a task only at its release time. In contrast, in our work we first assume a predictive
task model (e.g., periodic tasks) and so allows for design-time delay analysis and then
propose an online algorithm for mixed workload in hard real-time systems.
In [22, 32], optimal speed profiles were derived to achieve high resource utiliza-
tion. In [4, 33, 34], the use of the feedback control theory is proposed as a way to
implement adaptive techniques in the processor architecture. In [34], a predictive
19
frame-based DTM algorithm is presented. In [33]. a predictive DTM algorithm was
designed to improve the performance of multimedia applications.
There are also many other run-time thermal management techniques studied
for general-purpose applications. The authors in [4] perform extensive studies on
empirical DPM techniques for thermal management. Their results show that DVFS
can be very inefficient if the invocation time is not set appropriately. In [35], a thermal
model was presented that is capable of modeling cooling faults such as CPU fan or
case fan failures and load-balancing algorithms were designed based on this model.
In [36, 37, 38], temperature-aware floorplanning is used to place circuit blocks, such
that an even thermal profile is obtained.
System-level solutions have been defined to reduce the temperature in MPSoCs
using different scheduling mechanisms [39]. Finally, in [40], a detailed review of
thermal management techniques for multi-core architectures is presented.
Most of existing thermal management techniques are based on temperature mon-
itoring and tuning of microprocessor speed that do not result in optimal solutions.
Moreover, they do not provide a guarantee that the temperature constraints will be
satisfied at all instances of operation, which is critical for achieving system reliabil-
ity. Zhang and Chatha [41] addressed the knapsack problem for a given execution
sequence of jobs by assigning discrete frequency/voltage states. They proved that the
problem is NP-hard and proceeded to formulate a pseudo-polynomial optimal speed
assignment algorithm and a polynomial time approximation algorithm.
In [42], it classifies existing dynamic speed control algorithms for real-time sys-
tems into two categories. One is intra-task dynamic speed control algorithms, which
uses the slack time when a task is predicted to complete before its worst-case execution
time. The other is inter-task dynamic speed control algorithms, which allocates the
slack time between the current task and the following tasks. The difference between
20
them is that intra-task speed controlling strategies adjust the microprocessor speed
during an individual task boundary, while inter-task strategies adjust the speed task
by task. In most systems, it is difficult to predict well the earlier completion of tasks
before their worst-case execution time. We, therefore, consider inter-task dynamic
speed controlling strategy and the RSS scheme for the thermal management.
In our study, we focus our work on the efficient speed control to minimize the
response time of aperiodic workload in the presence of hard real-time periodic tasks
satisfying the temperature constraints.
E. Thermal Parameter Calibration
The performance-power optimization of processors using the speed control policies has
received considerable attention. Most of these research, however, does not consider
thermal constraints of systems. In the thermally-aware design domain, two impor-
tant subproblems can be considered: 1) Modeling the thermal behavior of systems
and 2) Designing methods to control processor performance and power consumption
to meet the temperature constraints. Several recent works have addressed the issue
of on-chip thermal modeling [38, 43, 44, 45, 46, 47, 48]. At the physical level, various
methods can be used to model the heat transfer in the substrate. Finite-difference
time domain [43], finite element [38], model reduction [44], random walk [45] and
Green-function [48] based algorithms have been applied for on-chip thermal analysis.
At the architectural level, [46] presents a thermal/power model for super-scalar ar-
chitectures. The work presented in [47] investigates the impact of temperature and
voltage variations across the die of embedded cores. Based on these and other simi-
lar models, Dynamic Thermal Management (DTM) techniques have been suggested
[4, 33, 34, 49]. A major impediment when putting proactive thermal management into
21
practice is the need to develop a thermal model that is appropriate for the platform
at hand. Generic thermal models only loosely capture the thermal behavior, due to
variability in fabrication, environmental effects, or the need for special configurations
of either cooling devices or other aspects of packaging. The models must therefore
be appropriately calibrated before use. In this study we describe an efficient method-
ology for parameterization of thermal models. It relies on an off-line analysis of a
reference application for the thermal behavior, which is based on the measurement of
the utilization behavior and the thermal behavior of the system at hand running the
application.
22
CHAPTER III
TRANSIENT OVERCLOCKING FOR APERIODIC TASK EXECUTION IN
HARD REAL-TIME SYSTEMS
A. Introduction
In this chapter we describe how transient overclocking can be applied to safely reduce
response times for aperiodic jobs in the presence of hard real-time periodic tasks.
To obtain mechanisms that are efficient at run-time, design-time method to allocate
overclocking budget to aperiodic workloads is proposed. This budget can then be
simply consumed at run-time similarly to that of a Deferrable Server [10] without
heeding to predict what the thermal effect of aperiodic-job execution is on the peri-
odics. Furthermore, there is no need to monitor the temperature of microprocessors
online with the management of overclocking budget.
This chapter will be organized as follows: In Section B, we will describe the
system model used in the chapter. We will present the thermal model, which describes
the interaction between processor speed and temperature. We will also describe
a basic dynamic speed control mechanism that can be easily applied for transient
overclocking. The task model will be described. In Section C we present the Transient
Overclocking Server. We describe the principles of operation and the design-time
computation of safe budget levels. In Section E we evaluate the performance of the
Transient Overclocking Server. Finally, we conclude the chapter in Section F with
summary and an outlook on unresolved issues.
23
Fig. 2. The critical instance of periodic tasks
B. System Model
The effect of transient overclocking on periodic tasks in a thermally constrained sys-
tem is defined by the thermal characteristics of the computational resources and of
the dynamic thermal management system, the specifics of the periodic task model,
and of the characteristics of the aperiodic job arrivals.
1. Thermal Model
The relation between processor speed and chip-level thermal behavior can be approx-
imated at first-order by the following Fourier Model as shown in Chapter II:
T ′(t) =κsα(t)
C− T (t)
R · C, (3.1)
where T (t) denotes the temperature at time t (with respect to the ambient tempera-
ture), and the processor speed s(t) at time t. The parameters R and C are the thermal
resistance and capacitance, respectively, and describe the thermal characteristics of
the chip.
24
2. Periodic Hard Real-Time Tasks
We consider a set of identical-period hard real-time tasks {Γi : i = 1, 2, . . . , n},
where each task Γi = (p, ci) has a minimum time period p between jobs and each job
requires ci processor cycles to complete in the worst case.1 We adopt a fixed-priority
scheduling scheme, and Γi is assigned priority i (the smaller the index, the higher the
priority).
To guarantee the schedulability of periodic tasks, we first determine the thermal
steady-state for the execution of periodic tasks. Figure 2 shows the critical instance
under the thermal constraint for identical-period tasks [21]: When the periods of
tasks are identical and no aperiodic jobs are present, the system can reach a worst-
case steady state, in which the temperature - call it T0 - at the period boundary is
maximized, and therefore the amount of time the system runs at high speed sH is
minimized. As a result, the schedulable utilization is minimized. Wang et al. proved
in [21] that, in a static-priority system, the critical instant for a medium-priority task,
say Γ2 in Figure 2, is when it is released in the thermal steady state together with all
higher-priority tasks, just after all lower-priority tasks just completed (and therefore
heated up the processor).
3. Aperiodic Tasks
The system shown in Figure 2 leads to two observations. Observation 1: The steady-
state is robust for periodic arrivals; whenever the execution time of a task invocation is
shorter than specified, or whenever the inter-arrival time of tasks exceeds the period,
the CPU may temporarily cool off. As a result, the speed control will kick in later
1We limit ourselves to identical-period tasks. The critical instance for arbitrary-period task set is an open problem. For general arrival curves we developed a boundon the critical instant in [23].
25
(a)
(b)
Fig. 3. Worst-case execution with aperiodic tasks
during the next busy period, and the steady state will eventually be reached again.
Observation 2: Any additional execution of (aperiodic) jobs disrupts the steady state:
the initial temperature at the beginning of the period increases, and less idle time for
processors remains. Figure 3 illustrates the effects of allowing increasing amounts of
aperiodic jobs to execute per period. Figure 3(a) shows how aperiodic and periodic
workloads can be executed together, with the aperiodic making use of transient over-
clocking in an RSS fashion2. Increasing the amount of aperiodic execution pushes the
completion time of periodic tasks back towards the end of the period. This in turn
prevents the CPU from cooling off after the busy period ends, which in turn triggers
the speed control to kick in earlier in the next period. As a result, the completion of
the periodic tasks is pushed back even further. As this happens, the opportunities for
transient overclocking disappear. Figure 3(b) shows the case where uncontrolled exe-
2In order to simplify the presentation, the illustrations in this paper display sys-tems with a small thermal capacitance with respect to periods and execution time.The results can be applied to thermally more inert systems by looking at multipleperiods.
26
Fig. 4. Thermal steady state of system
cution of aperiodic leads to the RSS system degenerating to a constant-speed system,
which executes at low speed throughout.
4. Thermal Steady State of System
In this section, we describe how to compute the durations of maximum and of equi-
librium processor speed to accommodate periodic and non-periodic workloads with
Reactive Speed Scheduling. We say that the temperatures at the beginning and end
of a period are equal in the thermal steady state. Based on the thermal model in Sec-
tion 1, we can derive the relations among durations, temperature, and the processor
speed.
Figure 4 shows one of the periods of a system that is in the thermal steady state
by an identical periodic task set and some amount of periodic budget consumption
for aperiodic jobs. According to the Fourier thermal model, the relationship among
the duration LH of the processor’s maximum speed execution, the temperature T0 at
the beginning of the period, and the processor speeds sE and sH can be expressed
using the following equation:
TE = TH + (T0 − TH)e−LH/τ , (3.2)
where TH = RκsαH , TE = RκsαE, and τ = RC.
27
(a)
(b)
Fig. 5. Erroneous slack computation leads to deadline miss
From (3.2), T0 can be expressed as
T0 = TH − (TH − TE)eLH/τ (3.3)
depending on the duration LH of the processor’s maximum speed execution in a
period. Similarly, the length of the idle time LD is also obtained from the thermal
model as follows:
LD = τ ln
(TE
T0
). (3.4)
Finally, the length LE of equilibrium-speed execution is expressed simply as
LE = p− (LH + LD), where p is the period of tasks which is identical for all tasks.
Thus, for any given single-period workload, the temperature T0 at the beginning
of a period and the durations of LH , LE, and LD in the thermal steady state of system
are obtained by the above relations based on the thermal model.
28
C. Aperiodic Task Servers and Transient Overclocking
For traditional real-time systems, Slack Stealer [9] is known to be an optimal aperiodic-
task server. When the system is thermally constrained, however, conventional ways
of slack computation without special consideration for temperature do not allocate
the proper amount of slack, which can lead to deadline misses. Figure 5 shows a
situation where a deadline is missed in a system with RSS for periodic and aperiodic
jobs. This is due to a slack computation that fails to consider thermal effects. In
this example, the slack allocated to aperiodic jobs should be used to compensate for
the transient overclocking portion at the beginning of the period. If an aperiodic
job used this slack, the periodics cannot take advantage of overclocking, and misses
the deadline (Figure 5(b). Since the example in Figure 5 uses an RSS scheme that
does not differentiate between periodic and aperiodic workload, the periodic job in
Figure 5(b) is penalized as it gets “crowded out” of the overclocking period, and thus
further delayed.
Accurate slack management in systems that use transient overclocking comes at
a high run-time overhead: Upon arrival of the aperiodic job, the amount of slack
must be computed based on:
• current temperature of the processor,
• current speed of the processor,
• remaining execution time of periodic jobs.
Since the relationship between current temperature and available slack is not linear,
due to the transient overclocking, this computation is too costly to be performed at
run-time: the slack stealer would have to predict when to transition from overclocking
back to equilibrium speed before computing the available slack. We therefore do not
29
expect on-line naıve slack stealers to be used in practice, despite their optimality. We
will propose an on-line thermally-aware slack stealer with the effort of minimizing the
overhead in next chapter.
1. Bandwidth Preserving Server under Thermal Constraint
Since slack stealing cannot be applied directly, we resort to a budget-based, bandwidth-
preserving scheme: In this chapter, we present the Transient Overclocking Server,
which allows for a very efficient management at run time of allocated budget to ape-
riodic jobs. Budget management needs only O(1) online computation using simple
consumption and replenishment rules: Whenever aperiodic jobs are ready and budget
remains, the budget is consumed at a pre-determined rate, and it is periodically re-
plenished to a pre-defined amount. In order to enable this efficient run-time operation,
the budget has to be computed offline. We partition the budget into two portions, an
overclocked portion BH of length LH (we call this loosely the “overclocking budget”)
and a non-overclocked portion BE of length LE. The processor is overclocked at speed
sH during the overclocked portion and runs at equilibrium speed sE during the rest
of the time, in addition to the idle time necessary to compensate for the overclocked
portion. In next section, we describe how to compute LH and LE and how to manage
the budget amount.
2. Design of Transient Overclocking Server
The offline computation of the overclocking budget BH presupposes a worst-case
steady state for the processor temperature. Figure 3(a) and Figure 3(b) indicate how
this steady state is linked to the overclocking budget.
30
3. Budget Computations
The budget is computed at design time by determining the lengths LH and LE of the
overclocked and non-overclocked portions, respectively. At run-time, the budget is
consumed in RSS fashion: first, any available overclocking budget BH is consumed,
followed by the non-overclocking budget BE.
Theorem 1. When we apply two different speed levels in the execution of a given
job with fixed durations of high-speed and low-speed of the processor, the amount of
temperature increase is the smallest when we have the order of ‘high-speed to low-
speed.’
Proof. Since the temperature variation by the change of processor speed and the
power thereof is interpreted into the linear RC-electric circuit model [35], the tem-
perature as an output to the power input can be superposed. Thus, the comparison
between temperature increases by two different orderings of speed assignment is same
as the description of Lemma 1 in [21] with a level of offset.
Lemma 1. [21] Given a time instance t, we consider a successive execution part of
job with a starting time t0 and the completion time t1, where t0 < t and t1 < t. We
assume the system is idle during [t1, t]. Define Tt as the temperature at t. If we shift
this part of job into a starting time t∗0 and a completion time t∗1 such that t0 < t∗0 < t
and t1 < t∗1 < t. Define T ∗t as the new temperature at t. Then we have Tt ≤ T ∗
t .
Based on the Lemma, running the processor at high-speed earlier than at the
other lower speed level increases the temperature less than the other way of speed
assignments.
Theorem 2. For a given thermal constraints, the RSS-style consumption of the bud-
get of which the budget consumption order is BH followed by BE, maximizes the
31
amount of processing clock-cycles that can be handled by the transient overclocking
server.
Proof. Suppose a fixed length of continuous CPU execution, l, composed of lH and
lE in written order, where lH is the duration of CPU runs with high speed sH and lE
is the duration of equilibrium speed sE. By the Theorem 1, if we reverse the order of
the execution durations to (lE, lH), the temperature at the end of the length becomes
higher. In the case, under thermal constraints, lH should decrease to satisfy the con-
straints. By the decrease of high-speed duration to l′H(l′H < lH), B
′H becomes smaller
than BH so that the total available budget B diminishes by the reverse ordering
of budget consumption. Thus the RSS-style consumption of the budget maximizes
the amount of processing cycles for the transient overclocking server under a given
thermal constraints.
In the following section we describe how to compute the amounts BH and BE of
overclocking and non-overclocking budget, respectively. We first describe the budget
computation in the absence of periodic workload. We then explain the integration
with periodic workloads.
a. Overclocking without Periodic Tasks
Overclocking Budget BH . Figure 6 shows three scenarios of arrivals of aperiodic
jobs that are sufficiently long to make use of all the available budget. The figure also
shows the resulting temperature curves and available clock cycles within a period
under a steady-state thermal envelope for the case of no periodic tasks. In the figure,
IH and IE are the maximum durations of speed sH and equilibrium speed sE so
that a steady-state temperature of T0 can be kept at the beginning of each period.
Although the duration of the overclocking portion, LH , changes depending on current
32
(a) Case 1
(b) Case 2
(c) Other Cases
Fig. 6. Temperature curves and available clock cycles
33
Fig. 7. Finding non-overclocking executing duration
temperature, the minimum safe length can be determined at system design time to
guarantee the thermal constraints.
Lemma 2. In the overclocking without periodic tasks, the maximum safe amount of
overclocking budget BH is min(L(1)H , L
(2)H ), where L
(1)H is the duration for the aperiodic
job is ready and executed from the beginning of a period until the temperature increases
to the critical level. And L(2)H is the duration for which the processor can run at sH
so that the temperature increases to the level T0 at the end of a period after some
processor idle duration.
Proof. We look at two cases, first.
Case 1: The aperiodic job is ready at the beginning of a period, as shown in Fig-
ure 6(a). L(1)H is easily computed, given the initial temperature, T0. LH then is equal
to IH in Figure 6(a). We obtain the solution from Equation (3.2):
L(1)H = τ · ln (TH − T0)
(TH − TE). (3.5)
Case 2: The processor is idle, and the aperiodic job arrives before the end of the
period. Since the processor is now overclocked until at least the end of the period,
the temperature rises quickly. As shown in Figure 6(b), the point of intersection be-
tween the decreasing thermal curve, Tdec(t), of the idling processor and the increasing
thermal curve, Tinc(t), of the overclocked processor has to be formulated to obtain
34
the length L(2)H . Tdec(t) and Tinc(t) are described as following equations;
Tdec(t) = T0 · e−t/τ . (3.6)
Tinc(t) = TH − TH · e−(t−δ)/τ , (3.7)
where δ = p− τ · ln( TH
TH−T0).
Thus, the intersection happens at tx = τ · ln(
T0+TH ·eδ/τTH
), and L
(2)H for Case 2 is
computed as the length L(2)H = p− tx.
Now, for other cases when the aperiodic job is ready to execute at a moment
different from that of the above two cases, the value for LH exceeds L(1)H and L
(2)H . That
is because the difference of current temperature at the moment and the temperature
it has to catch up to maintain thermal steady state is larger than that of two cases
above. No computation for other cases are therefore needed for LH . Thus, the
length LH is determined by comparing the two values for Case 1 and Case 2, LH =
min(L(1)H , L
(2)H ).
The overclocking budget BH is obtained by simply multiplying LH by sH .
Non-overclocking Budget BE. The duration LE is the length for which aperiodic
jobs execute at speed sE after the overclocking budget BH is exhausted. At that point,
the processor may continue to execute at speed sE for a while without violating the
thermal steady state. The amount of this non-overclocking budget BE varies over the
length of the period, as can be seen from Figures 7 and 8.
Lemma 3. In the overclocking without periodic tasks, non-overclocking budget BE is
bound approximately by the following function in a period
BE(t) = max(BE(0)− t · sE, BminE ), (3.8)
35
(a) No periodic tasks
(b) With periodic tasks
Fig. 8. Decrease of budget for aperiodic task server in period
where BE(0) = IE · sE.
Proof. Given the overclocking budget BH(LH), non-overclocking budget BE(LE) can
be computed to satisfy the thermal envelope built based on the pre-supposed thermal
steady state. At the beginning of the period, BE is the largest, as the processor
has the most time to cool off before the end of the period. As time progresses and
the processor idles, BE decreases, as the deferred execution of the entire budget
36
would cause T0 to be exceeded at the end of the period. Toward the end of the
period, BE is zero, as the execution of deferred overclocking budget BH would cause
T0 to be exceeded otherwise. Although the function decreases in convex shape, we
approximate it in linear fashion for the fast online computation. We denote the
approximate function as ”BE approximate” in Figure 8. That is, BE decreases at the
rate of sE (In other words, LE decreases at rate 1) while the system is in idle state
and the amount is larger than BminE . It is consumed at low speed rate, sE, whenever
BE is used for aperiodic jobs.
The minimum amount of BE is computed at the moment from which the succes-
sive execution of BH and BE makes the temperature at the end of a period be equal
to T0. Figure 7 shows the case for the computation of BminE .
In practice, towards the end of the period, both BH and BE are constrained by
time rather than temperature: Even for large value of B, there is not sufficient time
remaining in the period to consume the budget. For this reason, the value for BE in
Figure 8 is displayed as BE(t) = max(BE(0)− t× sE, BminE ).
b. Combining Periodic and Aperiodic Jobs
For the integration of the Transient Overclocking Server with periodic tasks, we
make three assumptions: First, all periodic tasks are schedulable in the system with
constant-speed (sE) scaling. That is, without aperiodic workload there is no need for
overclocking. Second, the periods of periodic tasks are identical. Third, for the sim-
plicity in handling the budgets, the budget replenishment period is set to be identical
to that of the periodic tasks.
We define two strategies for dealing with periodic tasks depending on whether
we allow to overclock the execution of periodic tasks as well, in addition to that of
37
(a) Case 1
(b) Case 2
Fig. 9. Temperature curves and available clock cycles: integration with periodic task
aperiodic jobs.
In the budget-sharing approach, both the periodic and aperiodic jobs can be
overclocked. If a periodic task becomes ready when no aperiodic job is in the queue,
it can make use of the overclocking budget, in the way described in Section a. While
this approach is very simple, it penalizes aperiodic jobs (in particular short ones) by
sharing the overclocking budget to the periodic tasks, which carry no benefit from it.
In the non-budget-sharing approach, the overclocking budget is used only for
aperiodic jobs, and the periodic jobs execute only at low speed, sE. Since we reserve
38
the overclocking for aperiodic jobs only, we achieve better average response times of
aperiodic jobs.
Lemma 4. In the case of budget sharing, the maximum available budget computed
in Section a is used both for periodic task and aperiodic task without ruining the
schedulability of periodic tasks.
Proof. Since the periodic task set is schedulable at constant low speed sE, it must be
schedulable after addition of the transient overclocking server as well. This is because
the overclocking server executes the periodic task at high speed as well in the way of
budget sharing so that the response time gets shorter. In this way, periodic tasks are
always schedulable in budget sharing strategy.
Lemma 5. For the non-sharing approach, the amount of maximum safe available
budget under thermal constraints is obtained by comparing two cases: either the ape-
riodic execution directly follows the periodic task set, or it directly preceeds the periodic
task set before the beginning of next period.
Proof. On the contrary to the case without periodic tasks, the available safe dura-
tions of sH and sE execution become shorter because the processor is heated by the
execution of periodic task before the start of budget consumption. With the higher
beginning temperature, the duration until the temperature hits the critical level ear-
lier than the case with no periodic task. Therefore, we need to look into cases that
aperiodic jobs are executed after the completion of periodic jobs in each period for
the computation of the available budget in the strategy. These cases are illustrated
in Figure 9. (We do not consider the thermal effect of back-to-back executions of the
aperiodic server since we are making sure that the temperature at the beginning of
the period does not exceed the the steady-state temperature T0).
39
The resulting budget allocation is illustrated in Figure 8(b). The length δpd in
the figure describes the execution duration of the periodic tasks. The computation of
budget follows the same way as that for the budget sharing approach except for the
thermal effects of δpd by periodic tasks.
D. Queueing Model
In this section, a queueing model for budget sharing approach is developed to analyze
the performance of the server under the thermal constraints. For a simple approxi-
mation, average processor speed, savg is introduced in the analysis.
Although there must be a little amount of error for the accurate response time
computation with the use of average processor speed, the error can be canceled out
by the probabilistic characteristic of aperiodic tasks and the effect of durations of sH ,
and sE is well reflected on savg.
With the average processor speed, savg, the queueing model analysis for the
transient overclocking server can be done in the same way as that for the conventional
slack stealing algorithm.
1. Arrivals and Computation Times of Aperiodic Task
• Arrivals of aperiodic tasks form a Poisson process with rate λ, i.e., the CDF of
inter-arrival time S of aperiodic tasks is [50]
FS(s) = 1− e−λs s ≥ 0. (3.9)
• The computation times of aperiodic tasks are exponentially distributed with mean
1/µ at sH , i.e., the computation time X of an aperiodic task is random with the CDF
40
LDLS
s(t)
sH
sE
savg
LH LE LD
LS
s(t)
sH
sE
savg
Fig. 10. Approximation using average processor speed savg
[50]
FX(x) = 1− e−µx x > 0. (3.10)
2. Modeling Transient Overclocking Server in Thermally Constrained Environment
Figure 10 illustrates how we simplify the effect of reactive speed scheduling by replac-
ing the multiple speed levels by an average processor speed to compute and approxi-
mate the average response time analysis for the aperiodic tasks.
The average processor speed is obtained using following equation:
savg = (sHLH + sELE)/LS , (3.11)
where LS = LH + LE.
From this point on with average processor speed, we are able to apply the conven-
tional way analysis of slack stealer except the processor-idle duration. In the design
of transient overclocking server under thermal constraints, the effect of the duration
is reflected on the average speed savg. That is, if LH is designed to be long, savg
increases, otherwise savg decreases 3.
Let Z be the first service time duration that an aperiodic task receives from
3We note that, due to the thermal constraints, the total amount of cycles availableduring interval LS is not constant with varying LH .
41
the transformed(averaged) transient overclocking server 4. Obviously, Z is a random
variable taking value between zero and SA (maximum available service duration in one
period by the transient overclocking server). The amount of Z is different depending
on the beginning moment of execution of the task in a period. The probability that
a server is busy can be approximated by λ/(
SA
p· η · µ
)using an M/M/1 queueing
model, where p is the budget replenishment period, SA is the maximum available
service duration in a period, and η is the ratio between savg and sH . Then, the
probability that Z is SA is 1− λ/(
SA
p· η · µ
). The distribution of Z other than the
case that Z is SA is then assumed to be uniform. Thus, the PDF of Z is expressed as
fZ(z) =
1−M2
SA
= M1, 0 ≤ z < SA
1− λ/
(SA
p· η · µ
)= M2, z = SA
. (3.12)
If a full-time server (no periodic tasks and no thermal constraints) handles aperi-
odic tasks, the mean response time can be easily obtained through an M/M/1 queueing
model. Because of periodic task execution and some idle duration, however, the ac-
tual service time is no longer an exponentially distributed variable. The actual service
time is expressed differently according to the beginning moment of execution of an
aperiodic job, as follows:
• 0 ≤ Z < SA,
X ′ = W +
(⌊W − Z
SA
⌋0
+ 1
)· (p− SA) , (3.13)
• Z = SA,
X ′ =
W, W ≤ Z
W − b+
{⌊W − Z
SA
⌋0
+ 1
}· (p− SA) , W > Z
, (3.14)
where X ′ is defined as the actual service time which means the delay between the
4In the development of this model we loosely follow an approach described in [51]for the simpler case of the Immediate Server.
42
beginning and the completion of the execution of the task. b is the beginning moment
of job execution. When we define X as the execution time of an aperiodic job at the
speed level of sH without any interference from periodic tasks, we set W = X/η as
the delay at the average speed, savg through an M/M/1 queueing model.
Equations (3.13) and (3.14) describe how to obtain the actual service time for the
given aperiodic job depending on the beginning moment of the job’s execution. This
enables us to determine the average response time for aperiodic tasks using a M/G/1
queueing model as explained in following section. In Equation (3.14), the variable
for beginning moment of job execution b is also assumed to be uniformly distributed
within its possible ranges. That is, fB(b) = 1/(p− SA) when b is within [0, p− SA].
3. M/G/1 Queueing Model
As shown in the above section, since the actual service time is no longer exponentially
distributed, an M/G/1 queueing model is required to compute the mean response time
Rm for aperiodic tasks. Rm is expressed as
Rm = E[X ′] +λE[X ′2]
2(1− λE[X ′])(3.15)
from [50].
From the PDFs of variables and Equations (3.13) and (3.14),
E[X ′] =
∫ SA
0
∫ ∞
0
X ′fX(x)fZ(z)dxdz
=
∫ SA
0
∫ ∞
0
X ′ηfW (w)fZ(z)dwdz (3.16)
and
E[X ′2] =
∫ SA
0
∫ ∞
0
X ′2ηfW (w)fZ(z)dwdz. (3.17)
43
Fig. 11. Comparison of average response times of aperiodic jobs without periodic task
In equations (3.16) and (3.17), we use the following expansion for an integral,∫ ∞
0
⌊W − Z
SA
⌋0
· ηfWdw =∞∑n=0
∫ (n+1)SA+z
nSA+z
n · ηfWdw, (3.18)
which is a similar approach described in [51].
E. Performance Evaluation
1. Simulations
In this section we evaluate the performance of the proposed Transient Overclocking
Server for various aperiodic arrivals alone or in combination with various periodic
workloads. We do this using a discrete-event simulation of a thermally-constrained
CPU that runs a single periodic task (which represents the worst-case periodic work-
load) and a Poisson stream of incoming aperiodic jobs.
To evaluate the Transient Overclocking Server, we run it with different overclock-
ing budgets and measure the response times experienced by the aperiodic jobs. In all
experiments, we vary the overclocking budget BH by varying the steady state temper-
44
(a) Budget-sharing approach
(b) Non-budget-sharing approach
Fig. 12. Average response time of aperiodic jobs with execution of periodic task: p =
200 msec
ature T0. This is represented by the value for IH on the x-axis, which represents the
time to reach the maximum temperature TC from the steady-state temperature T0.
In all figures except for Figure 12(b), IH is equal to LH , the length of the overclocking
budget.
The thermal parameters (thermal resistance R and thermal capacitance C) for
this evaluation have been experimentally derived through thermal monitoring of a
45
Lenovo T43 notebook with an Intel Pentium M CPU running at various speeds up
to 2.0GHz. Based on these parameters, we extrapolated the behavior of the same
processor at a hypothetical overclocked speed of 3GHz. We use the performance at
1.6GHz as the equilibrium speed sE and that at 3GHz as the overclocking speed sH .
We define the critical temperature to be 25oC above ambient temperature.
Figure 11 shows the effect of overclocking on aperiodic arrivals with different
job lengths. It clearly shows that systems with short aperiodic jobs (10msec in our
experiments) benefit from overclocking. In fact, the more aggressively we overclock
(IH large,) the better are the response times. This is easy to explain: for large
overclocking budgets (LH of 10msec and above) the aperiodic jobs can be executed
entirely within the overclocking budget, and therefore fully benefits from the increased
CPU speed. Long aperiodic jobs (50msec and 100msec in our experiments) show only
negligible reduction in response times, or have worse response times. Since these jobs
do not fit in the overclocking budget, and fit increasingly less into the non-overclocked
portion of the budget the more aggressively we overclock, they get penalized by the
reduced total execution time they have available during each period, and therefore
take more than one period to complete.
Figure 12 shows the effect of varying amounts of periodic workload on the re-
sponse times of the aperiodic jobs. In both graphs we use the “short” aperiodic
jobs from Figure 11 and add increasing amounts of periodic workload, starting from
zero, to 50msec execution time at overclocking speed sH . In both graphs we see how
large amounts of periodic workloads eventually “crowd out” the aperiodic workload
from the overclocking budget, and cause an increase in response time. The graphs
also show that the non-budget-sharing approach better protects the aperiodic jobs
by forcing the periodic jobs to run at equilibrium speed. The result is lower response
times in the non-sharing case.
46
In the case of very aggressive overclocking (IH of 20msec and higher) with high
levels of periodic workload (20msec execution time at sH and higher) a weakness of the
non-sharing approach becomes apparent: Since the executing time of the periodics
must be treated separately from the aperiodics, there is not sufficient slack left to
allocate a sufficiently large overclocking budget. In such cases, increasing IH actually
reduces the overclocking budget (in such cases L(1)H < L
(2)H ), and therefore increases
the response times.
2. Queueing Model Validation
We validated the queueing model against the discrete event simulations. Figure 13
and Figure 14 compare average response times obtained by the queueing model and by
simulations. As a simple way to validate our queueing model, we compare the values
at IH = 0. Having zero length of IH and no workload from periodic tasks means that
a CPU runs always at equilibrium speed sE and the transient overclocking server is
able to run whenever there are aperiodic tasks to execute without any interruption
of other tasks. We can take this way of working as a general M/M/1 at service rate
of µ · sEsH
. We can see that analytical and simulation results match the response time
by simple M/M/1 model at IH = 0. In Figure 13, we see that the results match each
other well with very small errors. With larger amounts of periodic task workload,
the effect of increasing the length of IH becomes severe, leading to large increases in
response time. From the comparison in Figure 14, we can also notice that the effect
by increase of IH is smaller than the simulations. Since we averaged two levels of
processor speed into savg, the response time appears to be less sensitive to the change
of IH relatively than simulations.
47
(a)
(b)
Fig. 13. Comparison of average response times between simulation and queueing model
without periodic task
F. Conclusion
By their very nature, embedded real-time systems are exposed to environmental ef-
fects, some of which can influence the ability of the system to provide the promised
performance guarantee levels. For example, atmospheric conditions may affect the
ability of free-space optical links to carry traffic (e.g., [52]), or electromagnetic inter-
48
ference may prevent 801.11-style networks to provide QoS guarantees [53]. Similarly,
service can be disrupted due to attacks by third-parties, software errors, changes in
security posture and other maintenance requirements, flash crowds, thermal influ-
ences, and many other reasons. Many of these environmental effects are outside of
the control of the system designer and operator5.
In contrast, other environmental effects that are triggered by system- or program
behavior, and for which therefore predictive models exist. Examples of this type
of environmental effects are: Thermal overload due to power dissipation, memory
availability in garbage-collected memory systems [54, 55], or energy availability in
battery-powered systems [56].
Such effects give rise to interesting priority inversions between tasks, where ac-
cess to the computational resource by one fully preemptible tasks may cause a higher-
priority task to miss its deadline in the future because of speed control. This interac-
tion is particularly interesting when it comes to handling of (supposedly low-priority)
aperiodic jobs. In this chapter we illustrate that traditional algorithms (such as Slack
Stealing and Deferrable Server) cannot be naıvely applied in thermally constrained
environments, as this can lead to missed deadlines. We then proceed to describe a
design-time scheme to allocate budget to accommodate aperiodic job arrivals. Finally,
we show how transient overclocking with the budget computed offline at design time
reduces response times for aperiodic jobs with a series of discrete-event simulations.
Many issues remain open after this work. For this paper we set out to define a
design-time approach to budget allocation for the Transient Overclocking Server under
thermal constraints. The benefit of using transient overclocking have been illustrated
5More precisely, we mean to say that the occurrence of events cannot be controlledby the operator or designer; the frequency of occurrences may be in some casescontrolled: for example, one can reduce the rate of software faults by better testing.
49
through experiments. Currently we have no tools available that support the engineer’s
decision on whether and how to apply transient overclocking. Analytical tools and
models must be developed that allow to optimize the budget allocation for given
settings.
In general, the type of priority inversions caused by the use of resources that later
need to be reclaimed (either through speed control, or garbage collection, or energy-
aware DVS, or others) needs to be better understood, and appropriate resource access
protocols need to be devised.
50
(a)
(b)
(c)
Fig. 14. Comparison of average response times between simulation and queueing model
with periodic task execution
51
CHAPTER IV
ON-LINE THERMALLY-AWARE TRANSIENT OVERCLOCKING FOR
MIXED-WORKLOADS
A. Introduction
In the previous chapter we described the design-time budget based transient over-
clocking method for mixed-workloads. The budget based approach guarantees ther-
mally safe execution of aperiodic jobs, and the approach is very efficient during run-
time with low overhead in the budget management and no need for on-line tempera-
ture monitoring. Since this speed control scheme effectively runs in open-loop mode it
can, however, be too conservative in minimizing the response times of aperiodic work-
load. This follows because the scheme computes budgets based on the assumption
that the system will be fully utilized at all times with worst-case periodic workload.
In addition it must assume that aperiodic jobs are always backlogged in the task
queue. In practical systems, however, the workload is often significantly lower, and
the temperature level is usually lower than the worst-case thermal levels as well.
In this chapter we propose an on-line thermally-aware transient overclocking
method to reduce the response times of aperiodic jobs efficiently at run-time. We
describe a modified Slack-Stealing algorithm to consider the thermal constraints of
systems together with the deadline constraints of periodic tasks. With the thermal
model and temperature data provided by embedded thermal sensors, we compute
slack for aperiodic workload (slack estimation) at run-time that satisfies both thermal
and temporal constraints. The slack estimation is based on the system thermal model,
thermal management strategy, and the microprocessor’s temperature monitored by
thermal sensors embedded. For the speed control policy, we consider inter-task speed
52
control scheme which adjusts the speed task by task. We also integrate the simple
Reactive Speed Scaling (RSS) as the thermal management strategy in which the speed
is switched to the equilibrium speed sE when temperature increases and reaches the
critical temperature Tc.
We will see in this chapter that the proposed Thermally-Aware Slack-Stealing
(TASS) algorithm minimizes the response times of aperiodic jobs accounting for the
lower temperature and the early completion of periodic tasks and it satisfies both the
thermal and the deadline constraints. Furthermore, the algorithm has low computa-
tional complexity with O(1) on-line computation for slack estimation per aperiodic
task arrival.
B. System Model, Assumptions and Notation
1. Assumptions and Notations
Throughout this chapter, we adopt preemptive Earliest-Deadline-First (EDF) [8]
scheduling policy. We assume that the computational workloads has two compo-
nents: A periodic task set with hard deadlines, and a set of soft deadline aperiodic
jobs. We follow standard practice and assume that the worst-case execution times
and the arrivals of periodic tasks are known a priori, and the execution times of soft
aperiodic jobs become known upon job arrival. We first propose a static solution for
aperiodic job executions, assuming that the execution times of the instances of all pe-
riodic tasks are equal to their worst-case execution times at all times, thus maximizing
the periodic tasks’ utilization. In practice, task instances often complete well before
their worst-case execution time. In such cases, service to aperiodic workload can be
increased or power consumption decreased by accounting for the unused scheduled
processor cycles. This is generally called dynamic slack reclamation [25, 57]. We will
53
Table II. Notations for Task ModelSymbol Meaning
Ut The total utilization of periodic task set at sE , that is, Ut =∑n
i=1eipi
Ue(s) The effective utilization of periodic task set at speed s, Ue(s) = Ut · sEs
sN Nominal CPU speed (which makes the effective utilization of the system beequal to 1)
Ji The ith aperiodic jobtri The arrival time of Jitfi The finish time of Ji
NTA The earliest next arrival time of a periodic task instance in the system aftertime t, which is equal to the next earliest deadline if pi = Di,∀Γi
c[t,NTA] The maximum amount of clock-cycles available from the current moment tuntil NTA by RSS
cpd The amount of periodic processing clock-cycles to execute until NTAcap The amount of aperiodic processing clock-cycles available until NTA
discuss the role of dynamic slack reclamation in the context of thermally constraint
systems and present a thermally-aware dynamic slack reclamation technique. As in
the previous chapter, all periodic tasks are assumed to be independent and in-phase.
The deadline of each periodic task instance is assumed to be at the end of the task
period.
Recall that the combination of RSS speed control and inter-task speed assignment
allows the system to adjust the processor speed at the following points: (a) at task
boundaries, (b) at each task arrival/finish instant, and (c) at the moment when the
critical temperature is reached.
In addition to the terms and notation defined in Chapter II, in the following we
will make use of the notation described in Table II.
2. Periodic Hard Real-Time Task Execution
We consider a set of hard real-time periodic tasks Γ = {Γ1,Γ2, . . . ,Γn}, where each
task Γi = (pi, ei) has a minimum time pi between job instances. Each job requires
54
ei execution time at equilibrium speed sE to complete in the worst-case. We adopt
the Earliest-Deadline-First (EDF) scheduling scheme to schedule the execution of the
periodic tasks. Given a set Γ of periodic tasks, we define the total utilization of Γ at
equilibrium-speed as Ut =∑n
i=1eipi. It is well known that Γ can be feasibly scheduled
by EDF if and only if Ut ≤ 1.0. We assume that the total utilization of the given
periodic task set is smaller or equal to 1.0, and so the task set is schedulable and
thermally safe at speed sE. Figure 15(a) shows an example of an EDF schedule and
the resulting temperature variation for a given task set Γ = {(10, 4), (30, 8)} at the
constant equilibrium speed sE. We also define the effective utilization (Ue) of the
periodic task set at speed s as follows:
Ue(s) =n∑
i=1
cis · pi
=n∑
i=1
sE · eis · pi
= Ut ·sEs
. (4.1)
When there is no aperiodic job to consider for scheduling, we decide to use the speed
which makes Ue(·) = 1. We call this speed level the nominal speed and denote it
by sN . We know that sN = Ut · sE, and that when Ue(sN) = 1, the task set Γ is
schedulable at speed sN by EDF. Figure 15(b) shows the EDF scheduling of the given
periodic task set Γ at the constant nominal speed sN . The advantages of the use of
nominal speed sN for periodic task set can be described in three respects: 1) As
research in energy-aware DVS schemes shows, the energy consumption is minimized
when a constant lowest-possible speed is selected for task executions [58, 59]. 2)
Lower speeds reduce the peak temperature during job executions, thus delaying the
triggering of the RSS thermal management mechanism. Finally, 3) When the speed
sN at which Ue = 1 is selected for periodic task execution, it facilitates the run-time
slack estimation since the amount of slack in the periodic workload is easily computed
without any reference to precomputed slack time tables.
55
(a) Scheduling with sE
(b) Scheduling with sN
Fig. 15. EDF scheduling with constant speed: Γ = {(10, 2), (30, 8)}
3. Aperiodic Task Execution
In systems with both periodic and aperiodic workloads, the latter must be scheduled
so as to minimize their response times while at the same time not causing deadline
violations for the periodic tasks.
A popular such scheduling algorithm is the Slack Stealing scheduler [9]. Slack
stealing executes aperiodic tasks by using the available slack times of periodic tasks.
56
If there is available slack in the periodic tasks, aperiodic jobs can be serviced first
without violating deadlines of periodic tasks as long as slack is available. The slack
times are computed on-line by the slack stealer with all the information about the
periodic task executions (e.g., periods, deadlines, remaining execution times, and
etc.). We call this computation slack estimation. It can be shown that slack stealing
minimizes the response times of aperiodic jobs [9].
In the following we base our thermally-aware scheduling on the Slack-Stealing
algorithm described in [9]. The slack stealer is particularly appropriate for aperiodic
job executions in our case because the algorithm can fully utilize the temporal re-
sources made available by the on-line slack estimation, which in turn minimizes the
response times of aperiodic jobs. In systems that provide multiple speeds, transient
overclocking can be applied to further reduce the response times of aperiodic jobs. By
temporarily increasing the microprocessor speed at times, more slack can be retrieved
and more clock-cycles during the slack can be allocated to aperiodic jobs.
While this form of transient overclocking is very efficient in the minimization of
the response times of aperiodic jobs, we need to take into account the thermal safety
of systems. That is, at any time during overclocking we need to keep track of the
current temperature in order to predict how much longer we can keep overclocking.
We call this the thermal slack in the system. As a result, in a thermally aware slack
scheduling we need to keep track temporal slack and thermal slack, and - if needed -
trade them off against each other.
Thus, when the system is thermally constrained, three issues arise in the appli-
cation of transient overclocking scheme:
• How fast and how long can the processor execute aperiodic jobs before thermal
constraints are exceeded ?
57
• How to compute the thermal slack ?
We propose the following thermally-aware slack-stealing algorithm. It is based on the
traditional slack-stealing algorithm and transient overclocking in a thermally aware
fashion.
-Γ11 Γ12 Γ13
sE
t0 4 10 14 20 24 30
-Γ21 Γ21 Γ21
sE
t0 4 10 14 20 24 26 30
(a) EDF scheduling of periodic tasks
-Γ11
Γ11Γ12 Γ21 Γ13 Γ21
J1
sE
sH
t0 26J1 released
8.6 10 14 20 24 306Γ21 missed deadline
dt
(b) Deadline miss by erroneous slack computation
-Γ11
Γ11 Γ21Γ12 Γ21 Γ13 Γ21
J1
sE
sH
t0 6J1 released
2 6 10 14 20 24 26 30
dt
(c) Conservative slack estimation: cpd = sE × (dt− tr1) = sE × 8.0
-Γ11
Γ11 Γ21Γ12 Γ21 Γ13 Γ21
J1
sE
sH
t0 6J1 released
2 10 14 20 24 30
dt
(d) Correct slack estimation
Fig. 16. Illustrations of slack computation: Γ = {(10, 4), (30, 14)}
Before providing the details of our approach, we show the necessity of using sN
58
for the slack estimation. The slack stealing algorithm estimates slack times using a
procrastination scheduling approach, where periodic task execution is delayed until
any slack is exhausted to maximize the duration of idle intervals. It therefore requires
the information of periodic task deadlines and the execution times of the tasks. The
conventional slack stealing algorithm creates a precomputed slack table and dynam-
ically updates the table to find appropriate slack time at run-time. In systems with
dynamic speed control, however, it would be very inefficient for the on-line slack es-
timation due to the computational overhead if we keep a precomputed slack table
or maintain the task execution history on the system as in the traditional way. In
this study, we propose an efficient on-line method to estimate slack in systems with
dynamic speed control. For the online slack estimation, we first need to set the instan-
taneous deadline dt by which the completion of specific amount of periodic workload
can be delayed without violating the deadline constraints of periodic tasks. In the
proposed method, we use the next task arrival NTA as the instantaneous deadline
for the slack estimation. With the instantaneous deadline dt set to NTA, we then
estimate the periodic workload amount of which we can delay the completion until dt.
When we correctly compute the periodic workload amount to complete by dt, we are
able to estimate the slack for aperiodic workload. However, the correct computation
of periodic workload to procrastinate requires the information of all the instances
of given periodic tasks and slack computation for each task instance, which will not
be appropriate for the on-line slack stealing under the system with dynamic speed
control. Instead, we decide to use the single time information of the instantaneous
deadline dt which is set to NTA. In addition, we introduce the use of the speed sN at
which Ue(·) = 1 for the on-line efficiency in slack estimation. By the use of the speed
sN , it will be shown that we can simplify the computation of how long to delay the
execution of periodic workload to benefit aperiodic job execution without having to
59
explicitly manage the slack table and the history of periodic task executions.
In the following after we describe the difficulty of correct slack estimation only
with the information of the next task arrival (NTA) by some scheduling examples, we
explain how the speed sN can be used to simplify the slack computation. We will then
illustrate why we need the thermal-awareness in the application of transient overclock-
ing scheme for the mixed-workload execution. We initially simplify the discussion by
not considering thermal constraints. Rather, we assume the aperiodic workload to be
executed at the highest speed sH (transient overclocking). To maximize the available
slack times, we also assume that CPU runs at sH for the periodic workload execution
between the release moment of aperiodic job tr and the instantaneous deadline dt.
In the proposed slack estimation method, when we do not take into thermal-
safety, the slack (in clock-cycles) can be simply computed at tr as follows:
slack = c[tr,dt] − cpd, (4.2)
where c[tr,dt] is the total number of clock cycles available at the speed sH during the
time interval [tr, dt], that is, c[tr,dt] = sH × (dt − tr). Recall that cpd denotes the
estimated periodic workload that needs to complete within the interval (tr, dt]. As
mentioned above, however, the correct computation of cpd is not trivial. First, it is
difficult to find on-line the proper set of periodic task instances to estimate slacks.
Second, the overhead of on-line slack computation for all task instances must be very
high.
In the following we illustrate the scheduling of newly arriving aperiodic tasks until
NTA to point out the issue of periodic workload estimation for the slack computation.
We use a task set with two tasks Γ1 and Γ2 :
p1 = 10, e1 = 4, p2 = 30, e2 = 14.
60
Figure 16(a) shows an EDF schedule of the periodic tasks. Suppose an aperiodic
job becomes ready at t = 2 at which point dt is set to NTA (t = 10). For the
estimation of the periodic workload that can be delayed until dt, we can think of using
the information about the periodic task instances currently in the EDF queue. The
naive use of task information in the take queue, however, results in deadline errors of
periodic tasks. Figure 16(b) shows the erroneous task schedule. In Figure 16(b), when
we take only the backlogged workload of Γ1,1 for the periodic workload cpd estimation
and do the slack estimation at t = 2, Γ2,1 would not have enough processing time to
complete and miss the deadline at t = 30. If, on the other hand, we consider both Γ1,1
and Γ2,1, which is backlogged in the EDF queue and regard them as the cpd for slack
estimation, we find no slack available until dt. In fact, the workload sum of Γ1,1 and
Γ2,1 is not able to be finished in the interval (2, 10] even at the highest CPU speed
sH if sH is assumed as sH = 1.5 · sE in this example. One possible solution for the
cpd estimation is, therefore, to simply multiply sE with the time interval between the
aperiodic job release moment tr and NTA. Although this way of periodic workload
estimation and the slack computation guarantees all periodic task deadlines, it does
poorly at reducing the response time of aperiodic workload. In fact, it significantly
overestimates the periodic workload to execute during the interval. In Figure 16(c),
we notice that very small amount of slack is retrieved at time t = 2 for aperiodic task
by estimating cpd = sE · (NTA − tr) = sE × 8.0, which leaves CPU idle during the
time interval (26, 30]. By the overestimation of periodic workload during the interval
(tr, NTA], the slack stealing algorithm becomes very conservative. On the contrary,
Figure 16(d) shows the correct slack estimation for the aperiodic job execution, which
leaves no idle time until the end of hyperperiod of Γ1 and Γ2 at t = 30. By estimating
the accurate minimum workload amount of Γ2,1 to complete until NTAs which satisfies
the deadline constraint of Γ2 in the example, we can retrieve the maximum amount
61
of slack for aperiodic workload at the moment t = 2.
However, the accurate estimation of the minimum periodic workload amount to
complete until NTA is not trivial in the case that the periodic task set is composed
of large number of periodic tasks. It should require a bookkeeping of periodic task
executions with a large memory space and high run-time computational overhead
which is not appropriate for on-line slack estimation. Furthermore, when the thermal-
awareness and the speed control scheme for thermal management is concerned, the
slack estimation becomes more complicated.
Therefore we apply the nominal speed, sN , to make the efficient and accurate
run-time estimation of periodic workload to execute for a specific time interval. By
the application of sN at which Ue(·) = 1, the periodic task set is always schedulable
under the EDF scheduling algorithm and the periodic workload to complete during a
specific interval (t1, t2] is computed simply as cpd = sN×(t2−t1). In following sections,
we will describe the slack estimation based on the nominal speed sN in detail.
Lastly, we show the necessity of thermal-awareness for the transient overclocking
scheme through another example of task scheduling. Figure 17 shows two different
EDF scheduling with aperiodic jobs with the use of sE or sH for aperiodic jobs and
sN for periodic workload. The speed assignment to periodic workload is assumed to
follow the conventional energy-aware constant speed algorithm by which the lowest-
possible constant speed is applied for given workload.
In the examples, the slack is computed simply by looking at every interval length
from the moment when an aperiodic job is released to an otherwise idle aperiodic job
server to NTA and supposing the CPU runs either at sE or sH during the interval.
In Figure 17(a) in which aperiodic workload runs at speed sE, the temperature never
reaches to the critical level Tc, it however delays the response time of aperiodic jobs.
When aperiodic jobs run at speed sH (Figure 17(b)), the response time is significantly
62
(a) Scheduling with sE
(b) Scheduling with sH
Fig. 17. EDF scheduling with aperiodic tasks: Γ = {(10, 2), (20, 8)}, λ = 0.1, µ = 0.5
reduced, but the thermal constraint cannot be satisfied. (In the example, we set
Tc = 80oC.)
In summary theses examples illustrate that the speed assignment for the exe-
cution of mixed workload must consider current thermal condition. Otherwise, it
either violates the microprocessor’s thermal constraint or unduly delays the response
times of aperiodic jobs. In the next section, we propose how to compute the slack
63
for aperiodic jobs with the application of RSS thermal management mechanism and
how to control the processor speed to minimize the response times of aperiodic jobs
satisfying both the deadline constraints of periodic tasks and the thermal constraints
of microprocessor.
C. Aperiodic Task Server with Transient Overclocking
As we showed in the previous section, any safe and effective slack computation method
must consider both the mechanism for thermal management and the temperature
variation. Although the use of the thermally safe constant speed sE guarantees both
the deadlines of periodic tasks and the thermal constraints, it is too conservative to
sufficiently reduce the response times of aperiodic jobs. We thus propose a thermally-
aware slack-stealing (TASS) algorithm to minimize the response times of aperiodic
jobs by fully utilizing the available slack without threatening the thermal safety of
systems.
1. Slack Stealing Server under Thermal Constraints
While the traditional slack stealing algorithm takes into account the slack in the
temporal dimension, any thermally aware slack-stealing algorithm must take into
consideration the thermal domain as well. [e.g. “One could informally say that such
an algorithm should account and trade-off timing slack and thermal slack.”] A slack
computation algorithm therefore requires a specific thermal model and the monitor-
ing of current temperature in addition to the available time interval to compute the
available slack. To better represent the temporal and the thermal dimensions, in
the following we will use the clock-cycles as the unit for the thermal slack. This is
in contrast to traditional slack computation algorithms, which account for execution
64
(a) Periodic workload estimation
(b) Temperature prediction
(c) Thermal slack estimation
Fig. 18. Basic idea of thermally-aware slack-stealing algorithm
time only. For the thermal model, we select the simple model represented in Equa-
tion 3.1. The thermal slack estimation is based on the projection of temperature
variations. First, the TASS algorithm predicts the temperature increase between the
current moment and NTA which is set as the instantaneous deadline. For the thermal
prediction, it considers the transient overclocking and the RSS speed control scheme
as a thermal management. It also assumes that the system is fully utilized during
the interval, that is, the CPU is continuously running in the interval. The TASS
algorithm then computes the total available clock-cycles c[tr,NTA] for the interval with
65
the reference to the projected thermal profile by which the high speed duration ∆tH
and the equilibrium speed duration ∆tE are obtained. Since the periodic workload
to complete within the interval, cpd, is estimated by the speed sN and the length of
the interval, we know the available slack amount by a simple arithmetic.
Figure 18 describes the basic idea how to find the thermal slack for aperiodic job
execution. At the release instant of aperiodic job, the system monitors the current
temperature Ttr at tr and find the moment of NTA (Figure 18(a)). With the tem-
perature Ttr , the time interval until NTA, and the thermal model, we then project
the thermal profile of RSS (Figure 18(b)). Based on the projected thermal profile,
we compute the total available clock-cycles c[tr,NTA] in the interval under RSS scheme
with the length of high speed execution ∆tH and the length of equilibrium speed
execution ∆tE. By the simple subtraction of cpd which is estimated in Figure 18(a)
from c[tr,NTA], we find the thermal slack cap (Figure 18(c)).
2. Thermal Slack Computation
Let Tss(s) denote the thermally steady-state temperature converged when the proces-
sor runs continuously for infinite time at a constant speed s. The time interval ∆tH
in Figure 18(b) after which the temperature reaches Tc at speed sH can be computed
by Equation 3.1 and is expressed as follows:
Tss(sH) = R · κsαH ,
∆tH =1
bln
(Tss(sH)− Tr
Tss(sH)− Tc
), (4.3)
where Tr is the monitored temperature at the moment of thermal prediction step (tr
in Figure 18). The value for ∆tH can be linearly approximated to lower the overhead
66
of run-time computation as follows;
∆tH =1
b
(Tc − Tr
Tss − Tr
). (4.4)
Observation 1. If we denote by ∆tH the value of ∆tH approximated by Eq. (4.4),
then ∆tH < ∆tH . The Thermally-Aware Slack-Stealing (TASS) algorithm guarantees
thermal safety of systems using the approximate value of ∆tH because it overestimate
the temperature increase while aperiodic job executes and less amount of clock-cyles
are assigned as slack to aperiodic tasks by the shorter length of maximum speed exe-
cution.
To simplify the run-time slack estimation, we decide to use ∆tH , the approximate
value of ∆tH , which is thermally safe according to the Observation 1. In the remaining
equations of this chapter, we use ∆tH for ∆tH unless there is a need to distinguish
those two terms. With the time length of the high speed duration ∆tH , the total
available clock-cycles c[tr,NTA] for the interval is computed according to the interval
length between tr and NTA as follows,
ctr,NTA =
sH ·∆tH + sE · (NTA− tr −∆tH) if NTA > (tr +∆tH),
sH · (NTA− tr −∆tH) otherwise.
Since we use the speed sN at which Ue(·) = 1 for the periodic task execution while
the TASS server is idle and the EDF schedule is applied, we guarantee that there
is no deadline violation of periodic tasks. Considering the EDF scheduling with the
nominal speed sN , we also know that the least amount of periodic task workload to
execute until NTA is cpd = sN · (NTA − tr) as seen in Figure 18(a). The largest
amount of aperiodic processing clock-cycles available until NTA, cap, is then simply
obtained as follows,
cap = ctr,NTA − cpd. (4.5)
67
In the next section, we describe how the proposed TASS algorithm works for the
mixed workload exectutions.
-Γ11 Γ21 Γ12 Γ21 Γ13 Γ22 Γ14 Γ22
sE
t0 2 5 7 8 10 12 15 17 18 20
(a) EDF scheduling of periodic tasks at sE
-Γ11 Γ21 Γ12 Γ21 Γ13 Γ22 Γ14 Γ22
sN= 0.8× sE
t0 2.5 5 7.5 10 12.5 15 17.5 20
(b) EDF scheduling of periodic tasks at sN
-Γ11 Γ21 Γ12 Γ12 Γ21 Γ13 Γ22 Γ14 Γ22
sN
t0 2.5 5 6 7.5 10 12.5 15 17.5 20
6
J1 released
cpd = 4.0 × sN
NTA
(c) An aperiodic job arrives at 6.0
-Γ11 Γ21 Γ12
Γ12
J1Γ21 Γ13 Γ22
Γ22J2
Γ14 Γ22
sNsE
sH
t0 2.5 5 6 7.5 10 12.5 15 17.5 20
6
J1 released
6
J2 released
NTA1 NTA2RSS
(d) Speed control by TASS for aperiodic jobs
Fig. 19. The schedule of TASS algorithm: Γ = {(5, 2), (10, 4)}
68
Algorithm 1 Thermally-Aware Slack Stealing(TASS): rules and algorithm
Input: Γ and J (Periodic task set and Aperiodic jobs)1: Compute sN by the total utilization, Ut, of periodic task set2: At every arrival of periodic task instance, update NTA3: begin4: TASS is initialized to be inactive5: while System is running do6: if J is in task queue then7: if TASS is inactive then8: wake up TASS9: cpd = sN · (NTA− tnow)
10: /* for dynamic slack reclamation */11: if cpd < cpd then12: cpd = cpd
13: end if14: end if15: TASS projects thermal envelope until NTA by RSS and computes ctr,NTA
16: cap = ctr,NTA − cpd
17: if cap > 0 then18: /*execute aperiodic job*/19: s=sH20: else21: if cpd > 0 then22: /*execute periodic job*/23: s=sH24: decrease cpd at speed rate s25: /*s may be switched to sE according to the thermal condition*/26: else27: /*CPU is idle*/28: s=029: end if30: end if31: else if Γ is in task queue then32: if TASS is active then33: s = cpd
NTA−tnow
34: if s > sE then35: /*execute periodic job*/36: s = sH37: end if38: decrease cpd at speed rate s39: /*s may be switched to sE according to the thermal condition*/40: else41: /*execute periodic job*/42: s = sN43: end if44: else45: s = 046: end if47: if tnow ≥ NTA then48: suspend TASS49: cpd = 050: end if51: /* Job selected executes at the assigned speed s. */52: /* Speed can be switched to sE by RSS when Tc is reached. */
53: end while
69
3. Speed Control
For the speed control, we focus on each time interval composed of two adjacentNTAs.
The algorithm of Thermally-Aware Slack Stealing (TASS) aperiodic job server is
explained in Algorithm 1 and the example is shown in Figure 19. At the beginning
of NTA interval, if there is no aperiodic job ready in task queue so that the TASS
server remains idle, the processor is assigned sN to execute periodic task instance as
described in lines 41-43 of Algorithm 1. When an aperiodic job is released at tr, the
TASS aperiodic job server becomes active and it projects a thermal profile based on
the monitored current temperature, the thermal model, and the RSS scheme (line
15). The TASS aperiodic job server is active until the next NTA is reached. If there
remains thermal slack cap, it executes the aperiodic job according to RSS strategy
(lines 17-19). And the remaining periodic task workload is also executed either by the
RSS scheme continuously or at the lowest possible constant speed according to the
the amount of workload (lines 21-24 and 32-39). When the aperiodic job completes
at tf without using up cap in the interval, times that were supposed to be consumed
for aperiodic job execution are reclaimed to lower the CPU speed for the remaining
periodic task execution. Suppose TASS server is active in the NTA interval and
there is no more aperiodic job ready in the aperiodic task queue. The lowest possible
constant to finish the remaining periodic workload cpd for the remaining time interval
[tf , NTA] is computed as spd = cpd
NTA−tf. If the speed is less than sE, we can safely
assign the speed spd for the periodic workload without any concern about the violation
of thermal constraint. Otherwise, we should make the speed control simply follow
RSS scheme for thermal safety (lines 32-39).
Figure 19 illustrates an example of TASS algorithm with the periodic task set
Γ = {(5, 2), (10, 4)}. Since Ut = 0.8, the nominal speed sN is set as sN = 0.8 · sE.
70
With sN , the effective utilization Ue becomes 1, and Figure 19(b) shows the EDF
scheduling of the given task set at the speed sN . At t = 6, we suppose an aperiodic
job is released (tr = 6.0), and TASS server becomes active to project thermal profile
until NTA (t = 10) and computes cpd(= 4.0 · sN). In Figure 19(d), we notice how
cap is estimated considering RSS thermal management mechanism. In Figure 19(d),
we also see that another aperiodic job J2 is released at t = 13 and serviced by TASS
aperiodic job server. In this case, however, it shows that there may not be the speed
switching to sE by RSS scheme during the executions of aperiodic jobs and of the
remaining periodic tasks until NTA depending on the thermal condition.
Fig. 20. Example of TASS speed control with temperature constraint Tc = 80oC:
Γ = {(10, 2), (20, 8)}, λ = 0.1, µ = 0.5
Figure 20 shows an example of aperiodic job scheduling by the proposed thermally-
aware speed control. In the example, the temperature never reaches over the critical
level Tc, while the response time of aperiodic jobs are significantly reduced by tran-
sient overclocking.
Lemma 6. Among all speed scaling scheme, the RSS minimizes the response times
71
of aperiodic jobs, when two discrete speeds are used 1.
Proof. Let acap denote the actual workload amount of aperiodic job released at tr.
From the Figure 18, suppose acap ≤ cap, then we need to run the CPU at the highest
speed possible to complete the aperiodic job at the earliest time. Thus, the RSS
scheme is the best to minimize the response time of the job.
On the contrary, if acap > cap, the aperiodic job cannot be finished by NTA and
the available slack clock-cycles within [tr, NTA] should be maximized to minimize
the remnant of the aperiodic job to execute in the following NTA intervals.
Let c denote the sum of the cycles by RSS in the interval. That is, c = cap + cpd.
And let TRSS be the temperature reached at NTA by RSS speed control. If there is
any other speed assignment using the two speeds (sH and sE) that retrieves c clock-
cycles and makes the final temperature TNTA be lower than TRSS, the speed control
must be superior to the RSS scheme retrieving more available clock-cycles than c by
the increase of high speed time length ∆tH , which increases TNTA to be equal to TRSS.
Assume that there is a way of speed assignment that is different from RSS scheme
and it satisfies the condition described above. Since the workload amount by the speed
assignment is assumed to be c, total time lengths of sH and sE in the interval must
be same as those of the RSS scheme, respectively. In this respect, the assumed speed
assignment can be regarded as a different combination of speed assignment orderings
from the RSS scheme, which is illustrated in Figure 21.
The comparisons of temperature increases by various orderings of speed assign-
ment can be understood by the comparison described in the Lemma 1 in [21] with
11) We simplify the thermally-aware slack-stealing mechanism and alleviate theoverhead of new speed computation by adopting two speed approach (RSS) for theaperiodic job execution. 2) We select two speeds sH and sE because the former isthe fastest speed when system temperature is low and the latter is the thermally safefastest possible speed when the temperature is at Tc.
72
(a) RSS speed control
(b) non-RSS speed control
Fig. 21. RSS scheme vs. non-RSS scheme for same amount of c[tr,NTA]
a level of offset. It is because the temperature is an output of the power input in
thermal-RC circuit model which is a linear-time-invariant system and can be super-
posed.
The Lemma 1 in [21] says that delaying some part of job execution increases
temperature more at a specific later time instance. And this can be directly inter-
preted as that running the processor at high-speed earlier decreases the temperature
lower at a moment after the execution of same amount of workload. For example,
given a current temperature Ttr and TRSS(= Tc), if we switch the speed assignment
ordering from < sH , sE > to < sE, sH > for the same amount of cycles (the execution
time length for sE and sH are ∆tE and ∆tH respectively) as shown in Figure 22, we
should see the thermal violation at NTA, that is, TNTA > Tc.
Based on the Lemma[21], we notice that there is no other speed assignment than
RSS to lower the temperature below TRSS at NTA obtaining c in the given interval.
73
Fig. 22. Switch of speed assignment
This is the contradiction.
For both cases i) acap ≤ cap and ii) acap < cap, therefore, we see the RSS scheme
is optimal for aperiodic job execution under thermal constraints.
Lemma 7. TASS algorithm guarantees both deadline constraints and the thermal
constraint of thermally constrained hard real-time systems.
Proof. For the deadline constraint to be satisfied in a hard real-time system with
EDF scheduling strategy, periodic task workload assigned to every NTA-interval is
required to complete within the interval. Since the periodic task workload is obtained
from the EDF schedule with a constant nominal speed sN that makes Ue = 1, the
thermally-aware slack-stealing strategy that considers the workload amount guaran-
tees the temporal feasible condition.
In every NTA-interval, if there is no aperiodic job ready and TASS is inactive,
system temperature never increases to Tc because the proposed algorithm assigns sN
which is equal or smaller than sE based on the assumption that the total utilization
74
Ut is equal or less than 1. When there is an aperiodic job released, RSS scheme is
applied until the next NTA is reached or the aperiodic job is complete, whichever
comes first.
For the execution of periodic workload while TASS server is active, too, unless
the constant speed adjusted is larger than sE, the system remains stable in thermal
respective. For the case that the required constant speed for the remaining periodic
workload until NTA is larger than sE, the system is also thermally safe since the
speed control follows RSS.
Therefore, both thermal constraint and deadline constraint are satisfied by pro-
posed thermally-aware slack-stealing speed control scheme.
Theorem 3. TASS algorithm is optimal for minimizing the response times of aperi-
odic jobs in thermally constrained hard real-time systems.
Proof. The task scheduling of mixed workload with TASS algorithm is feasible in
the sense that periodics meet deadlines and thermal constraints are satisfied by the
Lemma 7. And the Lemma 6 proves TASS minimizes the response times of aperiodic
jobs. Thus, TASS is regarded as the optimal algorithm for aperiodic jobs in thermally
constrained real-time systems.
4. Dynamic Slack Reclamation
For thermal slack computation, we consider both the temperature level of micropro-
cessor at the release moment of aperiodic job and the remaining periodic workload
to execute.
The slack computation described in section 2 is static because it considers only
the worst-case periodic workload. It is known that, in many cases, the instances of
real-time tasks complete earlier than the worst-case scenario. The earlier completion
75
of the instances of real-time tasks contributes to more slack achievement in two ways.
Less workload execution decreases temperature level after it is finished [21]. This
lower temperature eventually delays the moment of hitting the critical temperature
Tc and increases the length of high speed duration ∆tH in the equation (4.3). Further-
more, the early completion of periodic jobs means less remaining amount of periodic
workload than the worst-case scenario. Let the sum of the remaining worst-case pe-
riodic workload be denoted as cpd(tr) at the release instant tr of aperiodic task. Since
cpd(tr) is typically less than cpd by early completions of jobs in the NTA interval, we
can safely increase the thermal slack by replacing cpd with cpd(tr) in the equation (4.5)
without violating the deadline constraints of systems. By the increase of ∆tH due to
the lowered temperature level and by the decrease of remaining periodic workload to
complete until NTA, the slack cap for aperiodic workload increases.
Fig. 23. Example of an NTA interval and the NTA task queue
While the temperature decreases naturally by the early completions of periodic
workload, the worst-case periodic workload amount needs to be properly updated
and estimated at run-time according to the completions of periodic tasks. For the
management of the worst-case periodic workload in NTA intervals, we propose NTA
task queue which is a virtual periodic task queue. The NTA task queue holds the
76
periodic workload scheduling information at speed sN , which is based on the workload
information from actual periodic task queue. The NTA task queue is populated at
every beginning moment of NTA intervals and it accepts the workload scheduled only
for a single NTA interval. Thus, even when a periodic job is supposed to execute for
more than one NTA interval, only the portion of the workload which is supposed to
execute within the current NTA interval is queued in the NTA task queue. Figure 23
illustrates one NTA interval and the corresponding NTA task queue populated at the
beginning instant of the NTA interval. In the figure, we see only a portion of Γ2 is
queued in the NTA task queue.
The management of worst-case workload by NTA task queue is as follows:
- NTA task queue is populated only at the beginning moment of NTA intervals
based on the periodic task information in the actual periodic task queue of
systems.
- The periodic task execution is based on NTA task queue. That is, if NTA task
queue is empty, the system scheduler is not allowed to execute any periodic
workload even when the actual periodic task queue is backlogged.
- While periodic task executes, NTA task queue is updated accordingly. When
a periodic job is complete and removed from the actual task queue, the job is
also removed from NTA task queue.
- For the run-time slack computation, the sum of worst-case periodic workload
during a NTA interval is equal to the total sum of workload in NTA task queue.
Since the NTA task queue reflects early completions of periodic workload within
each NTA interval, we are able to reclaim the unused clock-cycles of periodic tasks
77
at run-time accordingly, which can reduce the response times of aperiodic workload
significantly.
This way of dynamic slack reclamation approach is sub-optimal under the ther-
mal constraints due to the possible non-work-conserving task scheduling. It should
be very efficient at run-time, however, with low computational overhead and with the
fact that we focus simply on every single NTA interval.
D. Experimental Evaluation
1. Simulation Model
We use the similar simulation environment as that used in [60]. Aperiodic tasks are
generated by the exponential distribution using inter-arrival time (1/λ) and service
time (1/µ) with parameters λ and µ. Changing the values of µ and λ, we control the
workload (ρ = λ/µ) of aperiodic tasks under a fixed utilization of periodic tasks, Ut.
There are four periodic tasks in Table III of which the total utilization is 0.4 as in
[60].
Table III. Periodic Task Set
Task Set (second)
Task Period WCET
Γ1 6 0.5
Γ2 8 1.0
Γ3 14 2.1
Γ4 18 3.1
Ut 0.4
The actual execution time of each periodic task instance is generated by a normal
78
distribution function in the range of [BCET, WCET], where BCET is the best-case
execution time. The mean and the standard deviation were set to (WCET+BCET )2
and
(WCET+BCET )6
, respectively [61].
In the experiment, the time delay of speed scaling overhead is assumed to be
negligible. For the simple comparisons of our proposed approach, we fix the maximum
speed sH to be 2.0 GHz. And the scaled (letting the ambient temperature Ta = 0)
critical temperature Tc is set to be 80oC.
To evaluate our proposed thermally-aware transient overclocking algorithm, we
also implemented non-slack-reclaiming static transient overclocking solution (NSR-
TO) and a constant speed (sE) slack stealing algorithm. For the constant speed
slack stealing algorithm, we compute slack supposing the application of sE both to
aperiodic job and to periodic job until NTA. For the constant speed slack stealing
solution as well, both the slack-reclaiming (SR-CSS) and non-slack-recaliming (NSR-
CSS) mechanisms are considered and the results are displayed for the comparison.
Figure 24 shows the results of the average response times of aperiodic jobs with
same periodic task set described in in Table III and changing the aperiodic task
densities (ρ = λµ). We fix BCET/WCET ratio γb/w of periodic tasks at 0.1. For
all experiments, the plots show that SR-TO scheme reduces the average response
time the most, which is very evident that SR-TO minimizes the aperiodic response
time by exploiting low thermal level and dynamic temporal slack reclamation. We also
notice that the slack-reclaiming (SR) schemes are much less sensitive to the increase of
aperiodic task density than the non-slack-reclaiming (NSR) schemes. That is because
SR schemes are still capable of getting more clock-cycles as slack by the dynamic
slack reclamation, while NSR schemes simply lose the available slacks according to
the increase of total system utilization with aperiodic jobs.
In Figure 24, we show the increase of average response times of aperiodic jobs
79
(a) 1µ= 1.0 (b) 1
µ= 2.0
(c) 1µ= 4.0 (d) 1
µ= 8.0
Fig. 24. Comparison of average response times according to various aperiodic task
density
according to the increase of the ratio between BCET and WCET (γb/w). Along with
the increase of γb/w, the difference of average response times between NSR schemes
and SR schemes decrease since the larger γb/w value means smaller temporal and
thermal slack to be reclaimed dynamically. In Figure 25, for the longer aperiodic
jobs (which present larger workload), we see more clearly the importance of dynamic
slack reclamations. For the short aperiodic job executions in low utilized systems, the
thermal-awareness plays an important in the reduction of response time of aperiodic
jobs (Figure 25(a)). For the long aperiodic job, on the contrary, the dynamic slack
reclamation appears to be more important (Figure 25(b)). This is because the highly
utilized systems result in higher average system temperature, and the higher the
average system temperature is, the less advantage of thermal-awareness there is.
80
(a) short aperiodic job executions, 1µ= 2.0
(b) long aperiodic job executions, 1µ= 6.0
Fig. 25. Comparison of average response times of aperiodic task
E. Conclusion
In this chapter, we have presented an Online Thermally-Aware Transient Overclock-
ing scheme for mixed workload in hard real-time systems. Under the thermally con-
strained hard real-time systems, conventional ways of aperiodic job executions with
no thermal consideration may result in either the thermal violation or very longer
delays of aperiodic job execution. If we apply the fastest thermally safe constant
speed for the aperiodic job execution as a very conservative way, it does not reduce
the response times of aperiodic jobs sufficiently because thermal slack is not used.
On the contrary, when the fastest processor speed is applied without the considera-
81
tion of thermal conditions, the aperiodic job executions should lead to critically high
temperature.
By the proposed Thermally-Aware Slack-Stealing algorithm, we compute the
slack for aperiodic jobs online efficiently considering both the temporal and thermal
constraints. A static approach which expects only the worst-case periodic workload
is first described and the dynamic approach of the slack reclamation method is pre-
sented.
Simulations results have shown that the Thermally-Aware Transient Overclock-
ing can effectively reduce the average response times of aperiodic workload and that
the thermal-awareness is more important in the minimization of aperiodic jobs when
the system is less utilized.
82
CHAPTER V
EFFICIENT CALIBRATION OF THERMAL MODELS BASED ON
APPLICATION BEHAVIOR
A. Introduction
In Chapter II, we described a number of dynamic thermal management (DTM) ap-
proaches that have been proposed, ranging from dynamic voltage and frequency scal-
ing (DVS) to clock gating and to architecture-level mechanisms that balance the load
across functional units or cores on the processor chip. Reactive DTM approaches trig-
ger appropriate thermal control actions (e.g. DVS or clock gating) whenever readings
from thermal sensors exceed a particular level [4, 21, 62, 63, 64]. Proactive DTM,
on the other hand, allows for optimal thermal control by predicting thermal trajec-
tories ahead of time as a function of CPU frequencies [65] and task executions [66].
While proactive DTM has been shown to allow for better utilization of computational
resources compared to reactive schemes [65], it is also significantly more difficult to
implement in practice. Most notably, its effectiveness relies on the accuracy of the
thermal model that underlies the prediction of the effects of speed scaling and task
execution on CPU temperature.
The thermal behavior of microelectronic circuits is typically modeled using vari-
ations of an RC circuit [67]. Examples of applications of such RC models can be
found in [35] for web farms, in [65] for optimal speed control, and in [68] as part of
the HotSpot thermal simulation.
A major impediment when putting proactive thermal management into practice
is the need to develop a thermal model that is appropriate for the platform at hand.
Generic thermal models only loosely capture the thermal behavior, due to variability
83
in fabrication, environmental effects, or the need for special configurations of either
cooling devices or other aspects of packaging. The models must therefore be ap-
propriately calibrated before use. Figure 26 illustrates the effect of different cooling
environments (high/low fan speeds vs. external fan) on the thermal trajectory. Note
that the thermal increase rate and the highest temperature level varies for different
types of cooling support even with the workload and the CPU remaining the same.
When the thermal management must deal with such variabilities, effective configu-
0 200 400 600 800 1000 1200 140040
45
50
55
60
65
70
time (sec)
tem
pera
ture
(C
elsi
us)
Temperature pattern according to fan effects
using low fan speedusing high fan speedusng the external fan
Fig. 26. Thermal trajectories with various cooling environments
ration and efficient calibration methods are needed to accurately parameterize the
thermal models that drive the predictive thermal control. Unfortunately, as thermal
models describe the relation between input power and thermal behavior, they rely on
the availability of a measurement of input power for parameterization purposes. Since
such measurements are typically not available at processor level in most systems, we
need to find alternative ways for thermal model calibration.
In this chapter we describe an indirect methodology for parameterization of ther-
mal models, which relies on the off-line analysis of the thermal behavior for a reference
application, for which we measure both the detailed utilization behavior (through
84
PAPI performance measure counters) and the thermal behavior (through thermal
sensors on the chip). We determine and later exploit a linear relation between en-
ergy consumption and utilization level to calibrate the thermal model for new target
applications by comparing relative utilization levels. This results in accurate thermal
model parameters without the need for power measurements.
This chapter is organized as follows: In Section B we give a brief overview of the
thermal model used in this paper and of its RC circuit representation. In Section C we
describe our indirect approach to estimate the parameters of the thermal model based
on measurements of a reference application (462.libquantum from the SPEC CPU
2006 benchmark suite in our case). We describe how we measure and use relative
utilization levels to calibrate the thermal model for new applications. Section D
describes how we expand both the thermal model and the calibration approach to
multicore processors, and Section E validates our approach with experimental results.
Finally, we conclude with a summary and an outlook in Section F.
B. System Model
Effective prediction of the thermal trajectory depends first on a faithful thermal
model and then on the accurate estimation and calibration of the specific parameters
of the model for the system at hand. In this section we describe our thermal model
and then proceed to elaborate on parameterization approaches that rely on power
measurements. In the following sections we will describe methods to estimate model
parameters at run time without the need to measure power.
85
1. Thermal Model
Thermal modeling of microprocessor circuits has traditionally applied variations of
the simple Fourier’s Law of heat conduction (e.g., [67, 62]). We assume that the
environment has a fixed temperature, and that temperature is scaled so that the
ambient temperature is zero. We define T (t) and P (t) as the temperature and the
power input at time t, respectively. Fourier’s Law is then expressed as follows:
T ′(t) =P (t)
C− bT (t) , (5.1)
where the parameters R and C are the thermal resistance and capacitance, respec-
tively, and capture the thermal characteristics of the processor chip under considera-
tion. The term b = 1/RC represents the power dissipation rate and is the inverse of
thermal time constant of the system.
Simple thermal situations such as described in Equation (5.1) are often repre-
sented as RC circuits. Figure 27 shows the thermal RC circuit for a single-core pro-
Fig. 27. Lumped RC thermal circuit model for a single-core processor
cessor, and it includes both the processor core and the packaging. We assume that
the initial temperature is T0, i.e., T (t0) = T0. If P is a constant power input level
86
during a task execution interval, then the core’s temperature can be approximated
by the thermal circuit model and Equation (5.1) as follows:
Tc(t) = Tss.c(1− e−bc(t−t0)) + (Tc.0 − Tp.0)e−bc(t−t0)
+ Tss.p(1− e−bp(t−t0)) + Tp.0e−bp(t−t0), (5.2)
where Tss.c = RcP and Tss.p = RpP are steady-state temperatures of core and package
respectively, bp is the power dissipation rate of the package, and bc is that of the core
itself. The above approximation is derived from the fact that the dissipation rate bc of
the core is much larger than that of the package, bp. This causes the core’s temperature
increase to be dominated by the core’s own thermal characteristic immediately after
the input power is first applied, and then the core’s temperature becomes dependent
on the package’s thermal characteristic [65]. Hence, the temperature increases very
quickly at the beginning and it slows down its increasing rate according to the increase
of the package temperature.
C. Thermal Prediction Based on Relative Utilization
Given a sampled thermal trajectory T (t) of a system, the thermal parameters Tss.c,
Tss.p, bc, and bp can be infered with help of Equation (5.2) if the input power P
is known. In most systems, accurate power measurements are not available, and
methods must be developed to capture the effect of input power onto the thermal
behavior of the system without relying on absolute values for power levels. In the
following we will describe how we use relative utilization levels to predict the thermal
behavior of systems with the help of off-line measurement of thermal trajectories. In
order to keep the following discussion simple, we limit ourselves to constant-speed
processors, where the power consumption is application dependent. The results can
87
be easily extended to the case of discrete processor’s speed levels, where the power
consumption is defined by the application and by the speed control module of the
system.
The application of non-linear regression of Equation (5.2) on a measured thermal
trajectory T (t) yields estimations for Tss.c, bc = 1/RcCc, Tss.p, and bp = 1/RpCp. We
note that the thermal model cannot be derived directly from the measurements, since
(a) we do not know the input power P , and (b) we would have to factorize the results
in order to get to the individual parameters. We therefore use an indirect approach
- based on relative utilizations - to predict the thermal trajectory without knowledge
of the input power level. We base our approach on the following observation:
Observation 2. Assume a system with a constant-speed processor, and two appli-
cations Γ1 and Γ2 that execute workload amounts X1 and X2 (measured in number
of instructions) during a given interval [0, t], respectively. Let E1 and E2 be the en-
ergy consumed by Γ1 and Γ2 during the same interval. The energy consumption ratio
ρe = E1/E2, is equal to the utilization ratio ρx = X1/tX2/t
= X1/X2.
0.85 0.90 0.95 10.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Avg.IPC Ratio
Ene
rgy
Den
sity
Rat
io
Energy Density Ratio vs. Avg.IPC Ratio(normalized by 462.libquantum measurement)
Fig. 28. Energy density vs. average IPC
The above observation is supported by experimental results. Figure 28 shows
88
that the energy ratio during a given interval is proportional to the average utilization
ratio for the same interval. The plot is derived from 30 sampled executions from 5
different benchmarks1. Li et al. make a similar observation about the relationship
between the average power and the utilization (IPC) in [69]. The energy density
(average power) was computed from Equation (5.2) and the dashed line shows a
linear regression of the data.
The simple relation between utilization ratio and energy consumption ratio can
be used to estimate the parameters T targetss.p and T target
ss.c of a new application Γtarget as
follows:
Calibration:
Step 1: Measure the thermal trajectory Tref (t) of the reference application Γref .
(In our case we use the SPEC CPU 2006 benchmark 462.libquantum because
of its constantly high utilization level.)
Step 2: Determine the parameters T refss.c , T
refss.p, bc.ref , and bp.ref from Tref (t), for
example through nonlinear regression.
Step 3: Measure the average utilization level IPCref of the reference application
Γref .
Run-Time Estimation:
Step 4: Measure the utilization level IPCtarget of the target application Γtarget.
Step 5: Predict the thermal trajectory Ttarget(t) using Equation (5.2) with param-
eters T refss.c ×
IPCtarget
IPCref, T ref
ss.p ×IPCtarget
IPCref, bc.ref , and bp.ref .
1We measure the utilization level using the PAPI ipc function of the PAPI per-formance monitoring library. At 1-second intervals, we call PAPI ipc to retrieve thecurrent instruction and cycle counter, respectively. From these values we can deter-mine a measure for the utilization of the processor.
89
(In the following we will use the notation bc/p to denote both bc/p and bc.ref/p.ref .) We
note that Step 1 to Step 3 form the calibration of the thermal prediction system and
are performed off-line to determine a reference level. They may need to be performed
when a system is deployed to account for environmental factors affecting cooling. For
systems with multiple speed levels this calibration may need to be run once for each
processor speed level. For systems with dynamic active heat dissipation mechanisms
(e.g. fans with multiple speed levels) the calibration may need to be repeated as
well to account for the multiple levels of thermal dissipation. Step 4 and Step 5 are
executed at run time to exercise the model for the target application.
We will describe later how the accuracy can be further improved by using smaller
discrete time intervals to better track application dynamics. The following equation
or inequality shows how the temperature can be approximated in terms of energy
consumption. That is,
T (t) =P
C
∫ t
0
e−b(t−x)dx+ T0e−bt (5.3)
≤ P
C
∫ t
0
dx+ T0e−bt (5.4)
=P · tC
+ T0e−bt =
E(t)
C+ T0e
−bt
⇐⇒ T (t) ≤ E(t)
C+ T0e
−bt , (5.5)
where Equation (5.3) is the solution of the Fourier Law in Equation (5.1) for a constant
input power P . For the transition from Equation (5.3) to Equation (5.4) we take
advantage of the fact that∫ t
0e−b(t−x)dx = 1/b(1 − e−bt) ≤ 1/b · bt. As a result, the
temperature can be approximated with help of the energy consumed during the time
interval [0, t], which we denote by E(t). Similarly, we approximate the term (1−e−bt)
in Equation (5.2) by the term bt, which allows for the following simplifications of the
90
equation:
Tc(t) ≤ E(t)
Cc
+ (Tc.0 − Tp.0)e−bct +
E(t)
Cp
+ Tp.0e−bpt
= RcbcE(t) + (Tc.0 − Tp.0)e−bct
+RpbpE(t) + Tp.0e−bpt . (5.6)
Thus, if we discretize a task execution period with the interval of length ∆, the
temperature variation is expressed by the energy consumption as follows in a recursive
way,
Tc((i+ 1)∆) ≈ RcbcE(∆) + (Tc(i∆)− Tp(i∆))e−bc∆
+RpbpE(∆) + Tp(i∆)e−bp∆. (5.7)
We note that bc and bp have been previously determined, and therefore e−bc/p∆
are constants.
Given the above thermal approximation based on the energy consumption, we
are able to estimate the thermal trajectory of any task execution as a result of mon-
itored IPC values. The selection of the interval length ∆ depends on the thermal
parameters bc and bp so that the error between the estimated and the real temper-
ature values be acceptably small. At the ith interval, the temperature error by the
energy approximation is described as follows,
error(i∆) = RcbcE(∆) +RpbpE(∆)
+(Tc((i− 1)∆)− Tp((i− 1)∆))e−bc∆
+Tp((i− 1)∆)e−bp∆
−RcP (1− e−bci∆)−RpP (1− e−bpi∆)
≤ RcbcP∆+RpbpP∆. (5.8)
91
Thus, suppose for example that ∆ = 1bp20
= 1bc10
, RcP = Tss.c = 20, and RpP =
Tss.p = 15, the maximum error is 2.75oC. And the error decreases with decreasing ∆.
1. Temperature Predictions for Tasks with Dynamic Utilization
The temperature approximation method represented in Equation 5.7 can be easily
extended to predict temperatures in systems where tasks display dynamic (i.e., time-
varying) utilization levels. We exploit the relation between utilization level and energy
consumption previously determined in Step 2 of the calibration. Given the estimated
average energy consumption Eref of the reference application, Equation 5.7 for the
thermal trajectory can be modified as follows:
Tc((i+ 1)∆) ≈ RcbcEref · ρipc,i + (Tc(i∆)− Tp(i∆))e−bc∆
+RpbpEref · ρipc,i + Tp(i∆)e−bp∆ ,(5.9)
where ρipc,i =IPCtarget(i)
IPCrefis the utilization ratio during interval i.
Although the selection of energy as a control factor and the local linearization
of the model result in an overestimation in terms of the temperature increase, we
will show in Section E that the error is acceptable for the thermal estimation by the
appropriate choice of timing discretization length. In addition, by safely overestimat-
ing the thermal trajectory, this methodology can be applied in thermal management
systems that require conservative handling of thermal behavior.
Figure 29 shows the temperature measurement of a benchmark, 462.libquantum
and nonlinear regression of the measurement to estimate thermal parameters of pro-
cessor. The figure also shows the thermal approximation by the proposed utilization-
based approach for 462.libquantum which is the reference for thermal estimations
of other applications shown in Section E.
92
0 100 200 300 400 500 600 700 800 90050
60
70
80
90
100
110
time (seconds)
Tem
pera
ture
(C
elsi
us)
Thermal estimation: 462.libquantum
measurednonlinear regressionWorkload based approximation
Fig. 29. Thermal parameter estimation & utilization based temperature approxima-
tion
D. Extensions of Thermal Prediction Model for Multicore
Fig. 30. A lumped RC thermal circuit model for dual core processors
In this section, we derive the estimation of thermal trajectories in dual-core
system. For the multicore systems, the RC thermal circuit can be derived as shown
93
in Figure 30. Each core’s thermal trajectory can be expressed as follows,
T1(t) = Rp(P1 + P2)(1− e−bpt) + Tp.0e−bpt
+R1P1(1− e−b1t) + (T1.0 − Tp.0)e−b1t
T2(t) = Rp(P1 + P2)(1− e−bpt) + Tp.0e−bpt
+R2P2(1− e−b2t) + (T2.0 − Tp.0)e−b2t,
(5.10)
where Cp, bp, and Tp.0 are thermal parameters and the initial temperature of the
packaging - for example the heat-sink contacts shared by both cores. Similarly to the
single-core case, we estimate the parameters as described in Section C based on the
thermal trajectory caused by a reference application (462.libquantum in our case)
on each core. Given the symmetric arrangement of cores in many architectures, one
may be tempted to use a system-level model for each core. However, due to variations
in fabrication and external asymmetries caused by the layout and the integration of
the system with external cooling mechanisms, each core is likely to have different
thermal characteristics. It is advantageous, therefore, to derive the thermal param-
eters separately for each core. Similarly to Equation (5.6), for the single-core case,
Equation (5.10) can be approximated in terms of energy consumption as well, i.e.,
T1(t) = R1b1E1 + (T1.0 − Tp.0)e−b1t
+Rpbp(E1 + E2) + Tp.0e−bpt
T2(t) = R2b2E2 + (T2.0 − Tp.0)e−b2t
+Rpbp(E1 + E2) + Tp.0e−bpt.
(5.11)
We note that Equation(5.10) indicates how the thermal behavior of each core is
affected by the other core’s input power and the temperature level throughout the
package.
94
E. Results and Analysis
1. Experimental Setup
We evaluate the proposed thermal model in a real-world CMP product. In order to
estimate each core’s working temperature individually, we develop a specific device
driver for accessing the Digital Thermal Sensor (DTS) in our multicore system at
runtime. The trigger point of these thermal sensors is not programmable by software
since it is set during the fabrication of the processor [70]. To validate our thermal
model, we conduct our experiments using the system described in Table IV.
Table IV. Experimental Systems DescriptionSystem
The number of cores 4 coresProcessor Intel Quad Core Q6600
Memory Size 1 GBOperating System. SUSE 10.3 (Kernel Version: 2.6.27)
2. Experimental Results
Figure 31 shows the measured temperatures and the comparisons with the predicted
thermal trajectories. The results show how the approximations match the measured
thermal trajectories.
We define the error as:
error =
√∑(tf/∆)i=0 | Tm(i∆)− Ta(i∆) |2
(tf/∆), (5.12)
where Tm is the measured temperature, Ta is the estimated value, and tf is the
measurement interval length in seconds. Table V shows the average error, which is
found to be at most 3.5oC for these benchmarks. Note that we should be able to
decrease the error when a shorter monitoring time interval is selected for IPC.
95
0 50 100 150 200 250 30040
50
60
70
80
90
100Thermal estimation : 400.perlbench
time (seconds)
Tem
pera
ture
(C
elsi
us)
measurementworkload based approximation
(a) 400.perlbench
0 50 100 150 200 250 300 35040
50
60
70
80
90
100Thermal estimation : 403.gcc
time (seconds)
Tem
pera
ture
measurementworkload based approximation
(b) 403.gcc
0 50 100 150 20040
50
60
70
80
90
100Thermal estimation : 429.mcf
time (seconds)
Tem
pera
ture
(C
elsi
us)
measurementworkload based approximation
(c) 429.mcf
0 100 200 300 400 500 600 700 800 90040
50
60
70
80
90
100Thermal estimation : 464.h264ref
time (seconds)
Tem
pera
ture
(C
elsi
us)
measurementworkload based approximation
(d) 464.h264ref
0 50 100 150 200 250 300 350 40040
50
60
70
80
90
100Thermal estimation : 471.omnetpp
time (seconds)
Tem
pera
ture
(C
elsi
us)
measurementworkload based approximation
(e) 471.omnetpp
0 10 20 30 40 50 60 70 80 9040
50
60
70
80
90
100Thermal estimation : 483.xalancbmk
time (seconds)
Tem
pera
ture
(C
elsi
us)
measurementworkload based approximation
(f) 483.xalancbmk
Fig. 31. The temperature estimation in Intel Quad-Core Q9650 processor
Figure 32 shows the experimental result for the dual-core case. In the experi-
ment, two different benchmarks, 464.h264ref and 462.libquantum were executed
on core 1 and core 2 concurrently. By the measured IPCs from each processor core,
96
Table V. Average Error of Utilization Based Thermal Estimation
Benchmark Avg.Error (oC)
400.perlbench 2.09
403.gcc 3.47
429.mcf 3.49
464.h264ref 1.73
471.omnetpp 0.98
483.xalancbmk 2.74
0 200 400 600 800 100045
50
55
60
65
70
75
80
85
90
Thermal estimation :464.h264ref on core1 and 462.libquantum on core2
time (seconds)
Tem
pera
ture
(C
elsi
us)
core1 measurementcore2 measurementcore1 approximationcore2 approximation
Fig. 32. The temperature estimation of two cores: 464.perlbench & 462.libquantum
we estimated the thermal trajectory of each core based on the Equation (5.11) and
compared the results with measured values.
F. Conclusion and Future Work
Many of today’s commercial computing systems and embedded devices do not have
support for monitoring of power and energy. While this is rarely a problem for energy
awareness (when in doubt, reduce speed), it becomes critical when attempting to
97
predict the thermal behavior of a system. In this paper we develop a thermal model
and a methodology for the efficient calibration of its parameters that does not rely
on explicit information about input power. Rather, we closely monitor the thermal
behavior of a well-known reference application on the given computing platform, and
we then take advantage of the tight relationship between processor utilization and
power consumption to predict the thermal trajectory for an unknown application
at run time. The benefits of this methodology are numerous: First, the thermal
characteristic of the computing platform can be explored after deployment time. For
example, the system may run the reference application during configuration or even
boot time and derive the thermal parameters shortly before run time. Next, it is
easy to run this step for different levels of active heat dissipation if so desired. For
example, the system may have a combination of on-package fans and case fans, which
may be operated independently of each other. For each combination of such operating
fans, the thermal characteristics of the system can be captured by the model and
the parameters derived separately, thus enabling the effective prediction of thermal
trajectories with dynamic active heat dissipation mechanisms. Finally, utilization
information is readily available at run time, for example through Instructions Per
Cycle (IPC) counter in PAPI.
In order to verify our thermal prediction model, we experiment with other bench-
mark applications for the prediction of temperature variations based on the IPC data
monitored at every second. The experimental results show that the predictions are
very close to the measurement of actual temperature values measured via Digital
Thermal Sensor (DTS) embedded in each core despite the overestimation error that
results from the energy-based approximation.
In the future work, we plan to extend the model to address IO-intensive appli-
cations, by better monitoring both reference and run-time application. This requires
98
better information to be available about the proportion of computation-intensive in-
structions vs. total number of instructions at every monitoring interval. Similarly, the
model must be extended to better reflect the thermal reality on the chip. In addition
to IPC, other system information, like cache-misses or memory accesses, need to be
considered for general applications.
99
CHAPTER VI
CONCLUSIONS AND FUTURE WORK
In this chapter, we summarize the major results of this research and discuss future
directions of this work.
A. Conclusions
The high level of power density and the resulting heat generation has become a critical
problem in the design of modern processors. Since many static hardware-level ther-
mal solutions (e.g., fans, heat-sinks, coolants, and etc.) can be expensive and hard
to implement, in particular on small-sized embedded systems, various run-time Dy-
namic Thermal Management (DTM) mechanisms have been researched. Most DTM
mechanisms are equivalent to the speed control of the processor and take advantage of
the fact that the power consumption is the source of heat generation, and the power
is regarded as a convex function of processor speed.
In our study, we focused on the dynamic speed control for the scheduling of
mixed workloads on thermally-constrained hard real-time systems. A mixed work-
load is composed of a periodic task set and a sequence of aperiodic jobs. In such
a system, we say that the workload can be feasibly schedulable if all the deadline
constraints of periodic task instances are satisfied without the maximum safe tem-
perature of the processor being exceeded. To minimize the response time of aperiodic
jobs, we presented Transient Overclocking as an approach by which we apply the max-
imum CPU speed to the execution of aperiodic jobs. However, uncontrolled transient
overclocking would lead to excessive CPU temperatures. Thus, the speed control has
two contradictory directions to achieve two objectives: While the use of higher speed
minimizes the response times of aperiodic jobs at the cost of temperature increase,
100
the use of lower processor speeds keeps the CPU temperature at lower levels. Our
aim in the study is to propose an appropriate thermally-aware speed control mech-
anism to execute the mixed workload to minimize the response times of aperiodic
workloads while satisfying both the deadline constraints of periodic tasks and the
thermal constraint of the system.
Our attention is also on the derivation of a correct thermal model that can in
practice be efficiently applied for the thermal management. Thermally-aware speed
control requires a specific thermal model. Given such a model, we still need to
calibrate it to account for various cooling environments and different thermal char-
acteristics of each system. Without a properly calibrated thermal model, thermal
trajectories are predicted incorrectly, and any predictive thermally-aware speed con-
trol will work incorrectly. In this study, therefore, we also propose an efficient way of
thermal model calibration based on application behaviors.
For this work, in Chapter II, we reviewed briefly the power model and the thermal
model on which the speed control is based. For the mixed-workload executions, the
traditional aperiodic task scheduling algorithms were also reviewed. The various
thermal management mechanisms and thermal modelings were summarized as well.
In Chapter III, we first described how transient overclocking can be applied to
safely reduce response times for aperiodic jobs in the presence of hard real-time peri-
odic tasks. We then proposed a design-time method to allocate overclocking budget
to aperiodic workloads and the performance was compared by the discrete event-
based simulator. The proposed design-time budget based method has the advantage
of low overhead at run-time. Without the need to monitor the temperature of micro-
processors at run-time, the scheme provides a safe overclocking budget to aperiodic
jobs.
In Chapter IV, we devised the on-line thermally-aware transient overclocking
101
scheme for mixed workloads. By the design-time method which always assumes the
worst-case workload, the thermal slack and the temporal slack are not efficiently used
for the reduction of aperiodic job response times. We proposed, therefore, Thermally-
Aware Slack-Stealing algorithm to derive the maximum instantaneous slack for ape-
riodic job execution without ruining the deadline constraints of periodic tasks or
overheating the microprocessor. With the application of the conventional energy-
aware DVS scheme to periodic task executions and through the thermal prediction
approximation, we could compute the available slack conveniently with low compu-
tational overhead. We showed the proposed on-line thermally-aware transient over-
clocking method outperforms other constant speed schemes guaranteeing the thermal
and temporal constraints.
In Chapter V, we describe an indirect methodology for parameterization of ther-
mal models. Based on the analysis of a reference application along with the measure-
ment of its utilization behavior and the thermal behavior, we calibrate the thermal
model for other applications by comparing relative utilization levels. We verified the
proposed approach of thermal model calibration by some experiments with various
benchmark applications for the prediction of temperature variations.
B. Future Work
Our research goal is to devise a thermally-aware dynamic speed control scheme for
mixed workload in real-time systems. The feasible dynamic speed control should be
based on the correct thermal model. We thus proposed an efficient methodology of
thermal model calibration, too. We believe that proposed dynamic speed control
scheme based on the thermal model calibrated will be very useful for the design of
practical thermally-aware real-time systems. Some issues remain open for further re-
102
search. For either off-line or on-line transient overclocking scheme, there is no accurate
analytical tool to help engineers’ speed control decision, for example, the performance
comparisons of various schemes were dependent on simulations. Although most re-
searches and the evaluation of task scheduling algorithms for mixed workload depend
on simulations, analytical tools and models are worth being studied and developed.
We believe they will help the design of optimal thermally-aware speed control and
the task scheduling algorithm at the design-time.
For the thermal model calibration methodology, we need to extend the approach
to apply for the IO-intensive applications, too. Besides the measurement of IPC
values for applications, there should be the consideration of other metrics like the
cache-miss ratios or the number of memory accesses to correctly estimate the system
operation effects on the microprocessor temperature.
103
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112
VITA
Youngwoo Ahn received his B.S. degree in electrical engineering from Seoul Na-
tional University, Korea in 1997 and his M.S. degree from Seoul National University,
Korea in 1999. During 1999-2004, he worked as a research engineer at LG Electron-
ics in Korea. He also worked as a researcher at Electronics and Telecommunication
Research Institute in Korea from 2004 to 2005. He graduated with his Ph.D. in elec-
trical and computer engineering from Texas A&M University in August 2010. His
research interests lie primarily in real-time operating systems, especially in designing
and analyzing task scheduling under resource constraints. He is also interested in
low-power system designs. He may be contacted at:
Department of Electrical and Computer Engineering
Texas A&M University
TAMU 3112
College Station, TX 77843-3112
U.S.A.
Phone: (979) 209-9387
Email: [email protected]